Chapter 10: Square

Square-based word problems are the third type of word problems covered in MATQ 1099, the first being linear equations in one variable and the second being linear equations in two or more variables. Quadratic equations can be used in the same types of word problems you found above, except that by working with the given data, you end up creating a quadratic equation. To find the solution, you must factor the quadratic equation or use a substitution.

Example 10.7.1

The sum of two numbers is 18 and the product of those two numbers is 56. What are numbers?

First we know two things:

[latex]\begin{array}{l} \text{minor}(S)+\text{major}(L)=18\Rightarrow L=18-S\\ \\ S\times L=56 \end{ Matrix}[/latex]

Substituting [latex]18-S[/latex] for [latex]L[/latex] in the second equation gives:

[latex]S(18-S)=56[/latex]

Multiplying gives:

[latex]18S-S^2=56[/latex]

Which rearranges to:

[latex]S^2-18S+56=0[/latex]

Second, factor this square to get our solution:

[latex]\begin{matrix}{rrrrrrl} S^2&-&18S&+&56&=&0 \\ (S&-&4)(S&-&14)&=&0 \\ \\ &&&&S&=&4, 14 \end{matrix}[ /Latex]

Because of this:

[latex]\begin{array}{l} S=4, L=18-4=14 \\ \\ S=14, L=18-14=4 \text{ (this solution is rejected)} \end{ Matrix}[/latex]

Example 10.7.2

The difference between the squares of two consecutive even numbers is 68. What are these numbers?

The variables used for two consecutive integers (odd or even) are [latex]x[/latex] and [latex]x + 2[/latex]. The equation to use for this problem is [latex](x + 2)^2 - (x)^2 = 68[/latex]. Simplifying these results:

[Látex]\begin{matriz}{rrrrrrrrrr} &&(x&+&2)^2&-&(x)^2&=&68 \\ x^2&+&4x&+&4&-&x^2&=&68 \\ &&&&4x&+&4&=&68 \\ &&&&&-&4&&-4 \\ \hline &&&&&&\dfrac{4x}{4}&=&\dfrac{64}{4} \\ \\ &&&&&&x&=&16 \end{matriz}[/latex]

That means the two integers are 16 and 18.

Example 10.7.3

Sally and Joey's age product is now 175 more than their age product 5 years ago. If Sally is 20 years older than Joey, how old are they currently?

The equations are:

[latex]\begin{matriz}{rrl} (S)(J)&=&175+(S-5)(J-5) \\ S&=&J+20 \end{matriz}[/latex]

Substituting S gives us:

[Látex]\begin{matriz}{rrrrrrrrrrrr} (J&+&20)(J)&=&175&+&(J&+&20-5)(J&-&5) \\ J^2&+&20J&=&175&+&(J&+ &15)(J&-&5) \\ J^2&+&20J&=&175&+&J^2&+&10J&-&75 \\ -J^2&-&10J&&&-&J^2&-&10J&& \\ \hline &&\dfrac{10J}{10 }&=&\dfrac{100}{10} &&&&&& \\ \\ &&J&=&10 &&&&&&\end{matriz}[/látex]

That means Joey is 10 years old and Sally is 30 years old.

For questions 1 through 12, write and solve the equation that describes the relationship.

- The sum of two numbers is 22 and the product of those two numbers is 120. What are numbers?
- The difference of two numbers is 4 and the product of these two numbers is 140. What are numbers?
- The difference of two numbers is 8 and the sum of the squares of these two numbers is 320. What are the numbers?
- The sum of the squares of two consecutive even integers is 244. What are these numbers?
- The difference between the squares of two consecutive even numbers is 60. What are these numbers?
- The sum of the squares of two consecutive even integers is 452. What are these numbers?
- Find three consecutive even integers such that the product of the first two is 38 greater than the third integer.
- Find three consecutive odd integers such that the product of the first two is 52 greater than the third integer.
- The product of Alan and Terry's age is 80 years higher than the product of their age 4 years ago. If Alan is 4 years older than Terry, how old are they currently?
- The product of Cally and Katy's ages is 130 less than the product of their ages in 5 years. If Cally is 3 years older than Katy, how old are they currently?
- The product of James and Susan's ages in 5 years is 230 more than the product of their ages today. How old are they if James is a year older than Susan?
- The product of the ages (in days) of the two newborn babies Simran and Jessie in two days will be 48 more than the product of their ages today. How old are the babies if Jessie is 2 days older than Simran?

Example 10.7.4

Doug went to a conference in a town 120 km away. On the way back, he had to slow down 10 km/h due to road works, which meant that the return journey took 2 hours. How fast did you drive on the way to the conference?

The first equation is [latex]r(t) = 120[/latex], which means [latex]r = \dfrac{120}{t}[/latex] or [latex]t = \dfrac{120} { r }[/Latex].

For the second equation, [latex]r[/latex] is 10 km/h slower and [latex]t[/latex] is 2 hours longer. This means that the second equation is [latex](r - 10)(t + 2) = 120[/latex].

Let's eliminate the variable [latex]t[/latex] in the second equation by substitution:

[latex](r-10)(\dfrac{120}{r}+2)=120[/latex]

Multiply both sides by [latex]r[/latex] to eliminate the fraction and we get:

[latex](r-10)(120+2r)=120r[/latex]

Multiplying everything gives:

[latex]\begin{matrix}{rrrrrrrrrr} 120r&+&2r^2&-&1200&-&20r&=&120r \\ &&2r^2&+&100r&-&1200&=&120r \\ &&&-&120r&&&&-120r \\ \hline &&2r^2&-&20r&- &1200&=&0 \end{matrix}[/latex]

This equation can be reduced by a common factor of 2, leaving us:

[latex]\begin{array}{rrl} r^2-10r-600&=&0 \\ (r-30)(r+20)&=&0 \\ r&=&30\text{ km/h oder }-20 \text{ km/h (rechazar)} \end{array}[/latex]

Example 10.7.5

Mark paddles 30 km down the river, then turns around and returns to his original location. The entire journey took 8 hours. If the current is 2 km/h, how fast would Mark row in still water?

If we allow [latex]t =[/latex] the time to row down the river, then the time to return is [latex]8\text{ h}- t[/latex].

The first equation is [latex](r + 2)t = 30[/latex]. The current accelerates the boat, which means [latex]t = \dfrac{30}{(r + 2)}[/latex], and the second equation is [latex](r - 2)(8 - t) = 30 [/latex] when the current slows the boat down.

We will remove the variable [latex]t[/latex] from the second equation by replacing [latex]t=\dfrac{30}{(r+2)}[/latex]:

[Latex](r-2)\left(8-\dfrac{30}{(r+2)}\right)=30[/latex]

Multiply both sides by [latex](r + 2)[/latex] to eliminate the fraction and we get:

[latex](r-2)(8(r+2)-30)=30(r+2)[/latex]

Multiplying everything gives:

[latex]\begin{matrix}{rrrrrrrrrrrr} (r&-&2)(8r&+&16&-&30)&=&30r&+&60 \\ &&(r&-&2)(8r&+&(-14))&=&30r&+&60 \\ 8r^2&-&14r&-&16r&+&28&=&30r&+&60 \\ &&8r^2&-&30r&+&28&=&30r&+&60 \\ &&&-&30r&-&60&&-30r&-&60 \\ \hline &&8r^2&-&60r&-&32& =&0&& \end{matrix}[/latex]

This equation can be reduced by a common factor of 4, giving us:

[Látex]\begin{matriz}{rll} 2r^2-15r-8&=&0 \\ (2r+1)(r-8)&=&0 \\ r&=&-\dfrac{1}{2}\ text{ km/h (rechazar) o }r=8\text{ km/h} \end{array}[/latex]

## Questions

For questions 13-20, write and solve the equation that describes the relationship.

- A train travels 240 km at a certain speed. When the engine was replaced with an improved model, the speed increased by 20 km/h and the travel time was reduced by 1 hour. What was the speed of each motor?
- Mister. Jones regularly visits her grandmother, who lives 100 km away. A new motorway has recently opened and although the car journey is 120 km long, it manages to go an average of 20 km/h faster and takes 30 minutes less travel time. What is Mr Jones' fare on the old route and on the freeway?
- If a cyclist had gone 5 km/h faster, it would have taken 1.5 hours less to cover 150 km. Find the speed of the cyclist.
- At a speed of 15 km/h, a public transport bus would have needed an hour less for 180 km. What was the average speed of this bus?
- A cyclist cycles to a hut 72 km up the valley and returns in 9 hours. Your return speed is 12 km/h faster than your outward speed. Find your speed back and forth.
- A cyclist traveled 120 km and returned in 7 hours. On the way back, the speed increased by 10 km/h. Find the speed of this cyclist going in each direction.
- The distance between two bus stops is 240 km. If the speed of a bus were increased by 36 km/h, the journey would take 1.5 hours less. What is the normal speed of the bus?
- A pilot flew 600 km at a constant speed. The next day, the pilot flew back to the starting point in a 50 km/h headwind. If the plane was airborne for a total of 7 hours, what was the average speed of the plane?

Example 10.7.6

Calculate the length and width of a rectangle whose length is 5 cm greater than its width and whose area is 50 cm^{2}.

First, the area of this rectangle is given by [latex]L\times W[/latex], which means that for this rectangle, [latex]L\times W=50[/latex], or [latex] (W+ 5 ) W=50[/latex].

By multiplication we get:

[Latex]W^2+5W=50[/Latex]

Which rearranges to:

[Latex]W^2+5W-50=0[/Latex]

Second, we factor this square to get our solution:

[Látex]\begin{Matriz}{rrrrrrl} W^2&+&5W&-&50&=&0 \\ (W&-&5)(W&+&10)&=&0 \\ &&&&W&=&5, -10 \\ \end{Matriz} [/Latex]

We reject the solution [latex]W = -10[/latex].

This means that [Latex]L = W + 5 = 5+5= 10[/Latex].

Example 10.7.7

If the length of each side of a square is increased by 6, the area is multiplied by 16. Find the length of one side of the original square.

There are two areas to consider: the area of the smaller square, which is [latex]x^2[/latex] , and the area of the larger square, which is [latex](x+12)^ 2[/latex] .

The relationship between these two is:

[latex]\begin{array}{rrl} \text{larger area}&=&16\text{ times smaller area} \\ (x+12)^2&=&16(x)^2 \end{array }[ / Latex]

Simplifying these results:

[Látex]\begin{Matriz}{rrrrrrrr} x^2&+&24x&+&144&=&16x^2 \\ -16x^2&&&&&&-16x^2 \\ \hline -15x^2&+&24x&+&144&=&0 \end{Matriz }[/Latex]

Since this is a problem that requires factoring, it's easier to use the quadratic equation:

[latex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a},\hspace{0.25in}\text{ onde }a=-15, b=24\text{ e } c=144[/latex]

Substituting these values gives [latex]x = 4[/latex] or [latex]x=-2.4[/latex] (rejection).

Example 10.7.8

Nick and Chloe want to surround their 24" x 32" wedding photo with doilies of the same width. The resulting photo and mat must be covered with a layer of 1 m^{2}one-sided archival glass. Find the width of the carpet.

First, the area of this rectangle is given by [latex]L\times W[/latex], which means that for this rectangle:

[Latex](L+2x)(L+2x)=1\text{m}^2[/Latex]

O, cm:

[Latex](80\text{cm}+2x)(60\text{cm}+2x)=10.000\text{cm}^2[/latex]

By multiplication we get:

[latex]4800+280x+4x^2=10.000[/latex]

Which rearranges to:

[latex]4x^2+280x-5200=0[/latex]

What it boils down to:

[Latex]x^2 + 70x - 1300 = 0[/Latex]

Second, we factor this square to get our solution.

It's easier to use the quadratic equation to find our solutions.

[latex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a},\hspace{0.25in}\text{ onde }a=1, b=70\text{ e }c =-1300[/latex]

Replacing the values in returns:

[látex]x=\dfrac{-70\pm \sqrt{70^2-4(1)(-1300)}}{2(1)}\hspace{0.5in}x=\dfrac{-70\pm 10\sqrt{101}}{2}[/látex]

[latex]x=-35+5\sqrt{101}\hspace{0.75in} x=-35-5\sqrt{101}\text{ (rechazado)}[/latex]

## Questions

For questions 21 through 28, write and solve the equation that describes the relationship.

- Calculate the length and width of a rectangle whose length is 4 cm greater than its width and whose area is 60 cm
^{2}. - Calculate the length and width of a rectangle whose width is 10 cm less than its length and whose area is 200 cm.
^{2}. - A large rectangular garden in a park is 120 m wide and 150 m long. A contractor is brought in to surround this garden with a brick walkway. If the area of the walkway is 2800 m
^{2}How wide is the sidewalk? - A swimming pool in a park is 10 m wide and 25 m long. A pool cover is purchased to cover the pool and overlap all 4 sides of the same width. If the covered area outside the pool is 74 m
^{2}, how wide is the overlap area? - In a landscape plan, a rectangular flower bed is laid out 4 m longer than it is wide. yes 60m
^{2}are needed for plants on the bed, what dimensions should the rectangular bed have? - If the side of a square increases by 5 units, the area increases by 4 square units. Find the length of the sides of the original square.
- A rectangular field is 20 m longer than it is wide and has an area of 2400 m
^{2}🇧🇷 Find the dimensions of the lot. - The length of a room is 8 m greater than its width. If the length and width increase by 2 m, the area increases by 60 m.
^{2}🇧🇷 Find the dimensions of the room.

## FAQs

### Can I learn maths at 40? ›

**Anyone of any age can learn as much math as they want as long as they do it in the correct order** (no sense starting at calculus when you haven't done precalc) and are willing to invest the time to really understand it.

**Can I learn math at 50? ›**

**You can start learning to any subject at any age of your life, as long as you are interested toward the subject age doesn't matter**. The quote you mentioned here " Mathematics is young man's game".

**What maths should an 8 year old know? ›**

Eight-year-olds are working on **adding and subtracting** with more sophisticated strategies, like "counting on" from the higher number for addition, or base-10 facts to compose or decompose numbers. Two-digit addition and subtraction is being explored too.

**At what age does math ability peak? ›**

The ability to do basic arithmetic peaks at **age 50**.

But the next time you try to split up a check, keep this in mind: your ability to do basic subtraction and division doesn't reach its apex until your 50th birthday. In other words, "there may not be an age where you're the best at everything," Hartshorne said.

**At what age do mathematicians peak? ›**

Simonton found that mathematicians make their best research contributions (which he defined as the ones mentioned most often by historians and biographers in reference books) at what many might consider doddering old age: **38.8**.

**Can you still learn at 60? ›**

Research shows that **older adults can still**: Learn new skills. Form new memories. Improve vocabulary and language skills.

**Is it too late to study at 60? ›**

If someone is over 60 they should be encouraged to embark on learning something new. **It's never too late to learn**.

**Is it harder to learn at an older age? ›**

A large body of research about aging tells us that as we cross the threshold into middle age, neural connections that receive, process and transmit information can weaken from age and disuse. **It may take us longer to learn new information**. We often can't think as sharply or as quickly.

**How do you solve age problems fast? ›**

**How to Solve Problems on Ages?**

- Age after n years = X + n.
- Age n years ago = X – n.
- n times the present age = nX.
- If ages in the numerical are mentioned in the ratio A:B, then A:B will be AX and BX.

**What is the easiest way to calculate age? ›**

The method of calculating age involves the comparison of a person's date of birth with the date on which the age needs to be calculated. The date of birth is subtracted from the given date, which gives the age of the person. **Age = Given date - Date of birth**.

### What level of math should a 10 year old be at? ›

They'll begin to **multiply fractions, learn more about decimals and be introduced to percentages**. They will be able to count in powers of 10 and round numbers up to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000. Don't worry if some methods that your child learns are new to you!

**How much math Should a 10 year old know? ›**

Ages 6 to 10 years: Learning math

Understand fractions and word problems by fourth grade. Tell time and understand the value of different denominations of money. **Count to 100 by ones, twos, fives and 10s**. Do basic addition and subtraction up to 20.

**What should a 9 year old be able to do academically? ›**

They're able to **write a story several paragraphs long on the same subject or an outline with a beginning, a middle, and an end**. They're able to read aloud and are reading more complex and longer books. They'll probably be able to learn from what they read and follow instructions.

**At what age are you the strongest? ›**

**Strength peaks at age 25**.

Your muscles are at their strongest when you're 25, although for the next 10 or 15 years they stay almost as hefty - and this is one of the traits that can be most easily improved, thanks to resistance exercise.

**At what age does IQ become stable? ›**

The average child's IQ is not stable until **around four years of age**. It may be much later in children who were born early or who have significant health issues.

**Who is the No 1 mathematician in the world? ›**

1. **Pythagoras**. The life of the famous Greek Pythagoras is somewhat mysterious. Probably born the son of a seal engraver on the island of Samos, Pythagoras has been attributed with many scientific and mathematical discoveries in antiquity.

**Are mathematicians born or made? ›**

Researchers have said that if one wants to be good at all types of math, they need to practice them all, and can't trust their innate natural talent to do most of the job for them.

**Is it too late to get better at math? ›**

According to a rather widespread idea, **mathematics is something you should pick up at a very early age and pursue throughout your entire life** to achieve any significant success either in it or in any adjoining disciplines like computer science.

**At what age is your brain the sharpest? ›**

Scientists have long known that our ability to think quickly and recall information, also known as fluid intelligence, peaks **around age 20** and then begins a slow decline.

**Is 70 too old to learn to drive? ›**

Research suggests older drivers are safer drivers. However many decades you may have under your belt, **it is never too late to learn to drive** – all you have to do is decide when you want to start.

### Does learning slow with age? ›

Age is often associated with a decline in cognitive abilities that are important for maintaining functional independence, such as learning new skills. **Many forms of motor learning appear to be relatively well preserved with age, while learning tasks that involve associative binding tend to be negatively affected.**

**What should you not do at 60? ›**

**Things to Never Do After Age 60, Say Experts**

- Let Yourself Get Too Lonely.
- Skip Your Vaccinations.
- Lose Track Of Your Blood Pressure.
- Skip Regular Exercise.
- Drink Too Much.

**What can I study at 55 years old? ›**

- Agile.
- Business Development.
- Business Operations.
- Change Management.
- Coding.
- Compliance & Risk.
- Cyber Security.
- Dental Assisting.

**Can a 65 year old go to university? ›**

**Most universities and colleges welcome mature students** for their commitment, experience and skills.

**What can a 60 year old learn? ›**

...

**Here are some things you might improve at with age:**

- Verbal abilities. ...
- Inductive reasoning. ...
- Visual-spatial skills. ...
- Basic math. ...
- Tuning out negativity. ...
- Being content.

**What happens to your brain as you age? ›**

As we age our brains shrink in volume, particularly in the frontal cortex. As our vasculature ages and our blood pressure rises the possibility of stroke and ischaemia increases and our white matter develops lesions. Memory decline also occurs with ageing and brain activation becomes more bilateral for memory tasks.

**Is it harder to learn after 40? ›**

Just as you may not run as fast or jump as high as you did as a teenager,**your brain's cognitive power—that is, your ability to learn, remember, and solve problems—slows down with age**. You may find it harder to summon once familiar facts or divide your attention among two or more activities or sources of information.

**Does problem solving improve with age? ›**

An important aspect of successful aging is maintaining the ability to solve everyday problems encountered in daily life. The limited evidence today suggests that **everyday problem solving ability increases from young adulthood to middle age, but decreases in older age**.

**What would be the person's age after 180 months if his current age is 28 years? ›**

What would be the person's age after 180 months if his current age is 28 years? There are 12 months in a year. Hence, 180 months is 15 years. If the person's current age is 28 years, then his age after 15 years would be **43 years** which is the required answer.

**What is the formula for time and work? ›**

Important Time and Work Formula

**Work Done = Time Taken × Rate of Work**. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work. If a piece of work is done in x number of days, then the work done in one day = 1/x.

### How can I guess my age and number? ›

To do a number trick to guess someone's age, start by asking them to use a calculator to multiply the first number of their age by 5. Then, have them add 3 before doubling the answer. Next, they should add the second number of their age. Finally, tell the person to subtract 6 and the answer will be their current age.

**How does the age trick work? ›**

The four-digit form of the age is what you will use as the actual age. (a)**Ask the subject what the first two digits of the new Age is.** **If you take those two digits and follow it up with 20, the result is the Magic Number**. So if the first two digits of their Age is AB, then the Magic Number is AB20.

**What is the 3 trick in math? ›**

Trick 3: Think of a number

**Subtract 3 with the result.** Divide the result by 2. Subtract the number with the first number started with. The answer will always be 3.

**What is my age if I was born in 2005? ›**

The number of years from 2005 to 2022 is **17 years**.

**How can I find the year I was born? ›**

To do this manually, you would need to know your exact current age and the date of the day when you're calculating it from. Then you can simple **subtract the number of years from the current year, number of days** and you will have found out your date of birth. Example 1: A is 32 years and 12 days old on 12 January 2021.

**What are the three ways to measure age? ›**

...

**The three primary methods are:**

- Radiation Measurement.
- Stratigraphic Superposition.
- The Fossil Record.

**What math should a 12 year old know? ›**

11-12 year olds are placing **decimals and fractions on number lines** and have been introduced to the concept of positive and negative numbers. The mathematical language around numeracy becomes increasingly complex at this stage. New terms such as 'prime', 'composite', 'factor' and 'multiples' are introduced.

**How smart should a 10 year old be? ›**

They should be able to read and understand books that are more challenging and mathematical problems, including fractions, word problems, and multiplication and division involving long numbers. Their curiosity is likely growing, and they might ask a lot of questions about the world around them.

**Can 5 year olds count to 100? ›**

Most 5-year-olds can recognize numbers up to ten and write them. **Older 5-year-olds may be able to count to 100** and read numbers up to 20. A 5-year-old's knowledge of relative quantities is also advancing.

**Can a 10 year old do calculus? ›**

**Apparently they can**. Here in the US, students don't get to algebra until the 7th or 8th grade, so teaching calculus to youngsters between ages 10 and 12 seems like a challenge.

### What maths should a Year 11 know? ›

Number - which will include decimals, percentages and fractions as well as the four basic operations (addition, subtraction, multiplication and division). Algebra - which will include equations and formulae. Shape and space (geometry) - which will include volume, area, co-ordinates and nets.

**At what age should kids identify numbers 1 10? ›**

Most children learn to recognize and count the numbers from 1 to 10 when they are **between 2 - 3 years of age**. Each child is different and will learn at their own pace. Practice with your child each day to improve their number fluency.

**How tall should a 9 year old be girl? ›**

Age (years) | 50th percentile height for girls (inches and centimeters) |
---|---|

8 | 50.2 in. (127.5 cm) |

9 | 52.4 in. (133 cm) |

10 | 54.3 in. (138 cm) |

11 | 56.7 in. (144 cm) |

**Is being 12 still a kid? ›**

The United Nations Convention on the Rights of the Child defines child as, "**A human being below the age of 18 years unless under the law applicable to the child, majority is attained earlier**.” This is ratified by 192 of 194 member countries.

**What skills can I learn at 40? ›**

**8 crucial career skills everyone should learn by 40**

- Focusing on service. Few professional skills are as essential as the ability to focus on bringing value and serving your team and organization. ...
- Adaptability. ...
- Active listening. ...
- Effective communication. ...
- Time-management. ...
- Tech-savviness. ...
- Collaboration. ...
- Mindfulness.

**What can I learn at the age of 40? ›**

**10 Lessons to Learn by Age 40**

- Setting Yourself Up For a New Year of Life.
- #1. Embrace the Journey.
- #2. Take the Leap.
- #3. Be Intentional and Live Powerfully.
- #4. Discipline Equals Freedom.
- #5. You Are Your Thoughts.
- #6. Failure Only Comes If You Quit.
- #7. Trust Your Intuition.

**What new skills can I learn at 40? ›**

**To get you started, here are some ideas on what you can learn and master, to excel even more at work and in life.**

- Negotiation skills. ...
- Public speaking and presentation skills. ...
- Assertiveness. ...
- Networking. ...
- Managing your personal finances. ...
- 4 TIPS TO LEARN NEW SKILLS.

**What can I study at the age of 40? ›**

...

**Here are some career after 40 years age**

- Teacher. ...
- Hairstylist. ...
- Dietitian. ...
- Cybersecurity. ...
- Social Worker. ...
- Veterinary Technician. ...
- Marketing Manager. ...
- Patient Advocate.

**Is 45 too old to start a new career? ›**

**Yes, it is possible to start a new career at 40** — or 50, or 60, for that matter. It might take some extra effort, but it's never too late to set new personal and professional goals and live a life that feels meaningful.

**Is being 40 old? ›**

Middle age is the period of age beyond young adulthood but before the onset of old age. The exact range is disputed, but **the general consensus has placed middle age as the ages of 40 to 60**. This phase of life is marked by gradual physical, cognitive, and social changes in individuals as they age.

### What can I study at 50 years old? ›

**The following degrees and majors are ideal for adults over 50.**

- Accounting. Accounting programs typically culminate in an associate's or bachelor's degree. ...
- Psychology. ...
- Nursing. ...
- Financial Planning and Economics. ...
- Early Childhood Education. ...
- Human Services. ...
- Public Administration. ...
- Art.

**Is 47 too old to go back to school? ›**

Answer: **It's never too late to go back to school**! Adult learners are a growing population within higher education.

**Is 43 too old to go back to school? ›**

Don't worry, **you're never too old to earn your degree**. It's becoming increasingly common for individuals 40 and over to go back to school.

**What should you not do after 40? ›**

**Things to Never Do After Age 40, Say Health Experts**

- Forgetting to Train the Brain.
- Poor Posture.
- Starting a Workout Program Too Fast.
- Stop Smoking.
- Not Monitoring Blood Pressure.
- Gaining Weight.
- Not Getting Screening for Low T.
- Ignoring Prostate Health & Not Getting Screened.

**What is the best career to start at 40? ›**

**25 best careers to start at 40**

- Real estate agent.
- Proofreader.
- Freelance writer.
- Translator.
- Consultant.
- Job Recruiter.
- Social media manager.
- Project or program manager.

**Is 40 too old to learn a new career? ›**

If you're 40, 50 or older and wondering, 'Is it too late to change careers? ', we say, **no!** We'll also give you tips for how to overcome your fears and make it happen. Find out what makes you happy at work – and pursue it for that new career at 40.

**What is a good degree for an older person? ›**

**Two of the most promising generalist degrees for older adults are:**

- Master of Business Administration (MBA): The MBA is an ever-popular degree for people looking to work their way up to leadership roles. ...
- Master of Healthcare Administration (MHA): Healthcare is rapidly changing.

**Is it worth it to study after 40? ›**

**All of the things you could learn, the greater career potential, and the sense of accomplishment that come with earning a college degree make it a worthwhile investment at any age**. You shouldn't let anything hold you back from continuing your education if it is something you want to do.

**What can I study at the age of 45? ›**

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