## Age Word Problems

Every now and then, we encounter word problems that require us to find the relationship between the ages of different people. Age word problems typically involve comparing two people’s ages at different points in time, i.e. at present, in the past, or in the future.

This lesson is divided into two parts. Part I involves age word problems that can be solved using a single variable while Part II contains age word problems that need to be solved using two variables .

Let’s get familiar with age word problems by working through some examples.

## PART I: Age Word Problems Solvable with One Variable

In 6 years , Tanya will be three times as old as Marcus.

Tanya’s age in 6 years = 3( Marcus’s age in 6 years )

With that in mind, we can easily construct our equation.

Going back to the problem’s question, how old is Tanya now?

Answer: Tanya is 36 years old.

In 6 years, Tanya will be three times as old as Marcus.

So, will Tanya be three times as old as Marcus in 6 years? The answer is Yes .

- Let {\textbf{\textit{h}}} = Hector’s age
- {\textbf{\textit{h} - 4}} = Bruce’s age, since he is 4 years younger than Hector

Twenty years ago , Hector’s age was 13 years more than half the age of Bruce.

Hector’s age 20 years ago = \Large{1 \over 2} ( Bruce’s age 20 years ago ) + 13

We’re now ready to solve for the unknown variable, h .

Therefore, Hector’s present age is {\textbf{42}} years old.

Answer: Hector is 42 years old and Bruce is 38 years old .

- Let {\textbf{\textit{k}}} = Kwame’s age
- {\textbf{\textit{k} - 13}} = Stella’s age, since she is 13 years younger than Kwame

Nine years from now , the sum of their ages will be 43 .

Answer: Kwame is 19 years old and Stella is 6 years old .

Let’s now verify if indeed the sum of Kwame and Stella’s ages in 9 years will be 43.

- Kwame’s age in 9 years: k + 9 = {\color{red}19} + 9 = {\textbf{28}}
- Stella’s age in 9 years: k - 4 = {\color{red}19} - 4 = {\textbf{15}}

Perfect! The total of their ages nine years from now is 43 so our answers are correct.

Now that we have our equation, let’s solve for x .

Answer: In 11 years , Mr. Cook’s age will be 24 years less than three times as old as his son.

- Mr. Cooks’s age in 11 years: x + 34 = {\color{red}11} + 34 = {\textbf{45}}
- Son’s age in 11 years: x + 12 = {\color{red}11} + 12 = {\textbf{23}}

So in 11 years, Mr. Cook will be 45 years old while his son will be 23 years old.

- Let {\textbf{\textit{a}}} = Annika’s current age
- {\textbf{\textit{a} - 4}} = Annika’s age 4 years ago
- {\textbf{\textit{a} + 6}} = Annika’s age 6 years from now

With this information, it’s easy for us to write our equation.

Our next step is to solve for the unknown variable, a .

Answer: Annika is currently 44 years old.

- Annika’s age 4 years ago : a - 4 = {\color{red}44} - 4 = {\textbf{40}}
- Annika’s age 6 years from now : a + 6 = {\color{red}44} + 6 = {\textbf{50}}

## PART II: Age Word Problems Solvable with Two Variables

Looking back at our problem, there are two significant statements that can help us find our answers.

1) The sum of Aaliyah and Harald’s ages is 28.

From this statement, we can create the equation below:

2) Four years from now, Aaliyah will be three times as old as Harald.

Meanwhile, the statement above can be translated into the following equation:

We now have two equations to solve.

First, we’ll use equation 1 to solve for a .

Next, we’ll replace a with 28 - h in equation 2 .

- Aaliyah’s present age: a = 28 - h = 28 - {\color{red}5} = {\textbf{23}}
- Harald’s present age: h = {\textbf{5}}

Answer: Currently, Aaliyah is 23 years old while Harald is 5 years old.

We then need to subtract 7 from their current ages to represent how old they were seven years ago.

1) The sum of the ages of Jaya and Nadia is three times Nadia’s age.

2) Seven years ago, Jaya was three less than four times as old as Nadia.

Therefore, our two equations are:

Let’s first focus on equation 1 and solve for y .

Taking the values of y and n , we have:

- Jaya’s present age: y = 2n = 2({\color{red}12}) = {\textbf{24}}
- Nadia’s present age: n = {\textbf{12}}

So, going back to our problem. How old are they now?

Answer: Jaya is 24 years old and Nadia is 12 years old.

1) The difference between the ages of Penelope and her son, Zack, is 34 .

2) In six years, Penelope will be four times as old as Zack’s age two years ago.

Let’s now work on equation 1 to solve for p .

Next, we’ll replace p with 34 + z in equation 2 then solve for z .

- Penelope’s current age: p = 34 + z = 34 + ({\color{red}16}) = {\textbf{50}}
- Zack’s current age: z = {\textbf{16}}

Going back to our original question, how old are they now?

Answer: Penelope is currently 50 years old while her son, Zack, is 16 years old.

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- Age Problems
- Preliminaries
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- Quiz: Word Problems

Here are some examples for calculating age in word problems.

Now, use the problem to set up an equation.

Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa?

Therefore, Lisa is 7 years old.

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## 7.9 Age Word Problems

- The first sentence tells us that Joey is 20 years younger than Becky (this is the current age)
- The age change for both Joey and Becky is plus two years
- In two years, Becky will be twice the age of Joey in two years

Using this last statement gives us the equation to solve:

- The first sentence tells us that Carmen is 12 years older than David (this is the current age)
- The second sentence tells us the age change for both Carmen and David is five years ago (−5)

Filling in the chart gives us:

The last statement gives us the equation to solve:

Five years ago, the sum of their ages was 28

Therefore, Carmen is David’s age (13) + 12 years = 25 years old.

- The first sentence tells us that the sum of the ages of Nicole (N) and Kristin (K) is 32. So N + K = 32, which means that N = 32 − K or K = 32 − N (we will use these equations to eliminate one variable in our final equation)
- The second sentence tells us that the age change for both Nicole and Kristen is in two years (+2)

In two years, Nicole will be three times as old as Kristin

If Nicole is 25 years old, then Kristin is 32 − 25 = 7 years old.

- The first sentence tells us that Louise is 26 years old and her daughter is 4 years old
- The second line tells us that the age change for both Carmen and Louise is to be calculated ([latex]x[/latex])

In how many years will Louise be double her daughter’s age?

In 18 years, Louise will be twice the age of her daughter.

For Questions 1 to 8, write the equation(s) that define the relationship.

- Rick is 10 years older than his brother Jeff. In 4 years, Rick will be twice as old as Jeff.
- A father is 4 times as old as his son. In 20 years, the father will be twice as old as his son.
- Pat is 20 years older than his son James. In two years, Pat will be twice as old as James.
- Diane is 23 years older than her daughter Amy. In 6 years, Diane will be twice as old as Amy.
- Fred is 4 years older than Barney. Five years ago, the sum of their ages was 48.
- John is four times as old as Martha. Five years ago, the sum of their ages was 50.
- Tim is 5 years older than JoAnn. Six years from now, the sum of their ages will be 79.
- Jack is twice as old as Lacy. In three years, the sum of their ages will be 54.

- The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary.
- The sum of the ages of a father and son is 56. Four years ago, the father was 3 times as old as the son.
- The sum of the ages of a wood plaque and a bronze plaque is 20 years. Four years ago, the bronze plaque was one-half the age of the wood plaque.
- A man is 36 years old and his daughter is 3. In how many years will the man be 4 times as old as his daughter?
- Bob’s age is twice that of Barry’s. Five years ago, Bob was three times older than Barry. Find the age of both.
- A pitcher is 30 years old, and a vase is 22 years old. How many years ago was the pitcher twice as old as the vase?
- Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now?
- The sum of Jason and Mandy’s ages is 35. Ten years ago, Jason was double Mandy’s age. How old are they now?
- A silver coin is 28 years older than a bronze coin. In 6 years, the silver coin will be twice as old as the bronze coin. Find the present age of each coin.
- The sum of Clyde and Wendy’s ages is 64. In four years, Wendy will be three times as old as Clyde. How old are they now?
- A sofa is 12 years old and a table is 36 years old. In how many years will the table be twice as old as the sofa?
- A father is three times as old as his son, and his daughter is 3 years younger than his son. If the sum of all three ages 3 years ago was 63 years, find the present age of the father.

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## Algebra: Age Word Problems

## How To Solve Age Word Problems?

## How To Solve Age Problems Involving A Single Person?

Example: Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

Step 2: Write out the equation.

Answer: John is now 18 years old.

## How To Use Algebra To Solve Age Problems?

- Ten years from now, Orlando will be three times older than he is today. What is his current age?
- In 20 years, Kayleen will be four times older than she is today. What is her current age?

## How To Solve Age Problems Involving More Than One Person?

Solution: Step 1 : Set up a table.

Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.

Write the new relationship in an equation using the ages in 5 yrs.

In 5 years, John will be three times as old as Alice.

2 x + 5 = 3 ( x – 5 + 5) 2 x + 5 = 3 x

Answer: Peter is now 5 years old.

Solution: Step 1: Set up a table.

Let x be John’s age now. Add 2 to get the ages in 2 yrs.

Write the new relationship in an equation using the ages in 2 yrs.

In two years time, the sum of their ages will be 58.

Answer: John is now 8 years old.

## How To Solve Word Problems With Multiple Ages?

- Sally is 3 times as old as John. 8 years from now, Sally will be twice as old as John. How old is John?
- Kim is 6 years more than twice Timothy’s age. 2 years ago, Kim was three times as old as Timothy. How old was Kim 2 years ago?
- Leah is 2 less than 3 times Rachel’s age. 3 years from now, Leah will be 7 more than twice Rachel’s age. How old will Rachel be in 3 years from now?
- Becca is twice as old as Susan and Greg is 9 years older than Susan. 3 years ago, Becca was 9 less than 3 times Susan’s age. How old is Greg now?
- Lauren is 3 less than twice Andrew’s age. 4 years from now, Sam will be 2 more than twice Andrew’s age. 5 years ago, Sam was three times Andrew’s age. How old was Lauren 5 years ago?
- Gabby is 1 year more than twice Larry’s age. 3 years from now, Megan will be 27 less than twice Gabby’s age. 4 years ago, Megan was 1 year less than 3 times Larry’s age. How old will Megan be 3 years from now?

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## Unit 6: Lesson 6

## Age word problem: Ben & William

- Age word problem: Arman & Diya
- System of equations word problem: walk & ride
- System of equations word problem: no solution
- System of equations word problem: infinite solutions
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: apples and oranges
- Systems of equations with substitution: coins
- Systems of equations with elimination: coffee and croissants
- Systems of equations: FAQ

## IMAGES

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## COMMENTS

You may notice that Tanya's current age is defined using the age of Marcus. However, Marcus's present age is currently unknown. So let's express Marcus's age

First, circle what it is you must ultimately find— how old is Tom now? Therefore, let t be Tom's age now. Then three years ago, Tom's age would be t – 3. Four

If the age of a person is 'x', then 'n' years after today, the age = x + n. Similarly, n years in the past, the age of this would have been x – n years. Example

One application of linear equations is what are termed age problems. When solving age problems, generally the age of two different people (or objects) both

Steps to Solve Age Word Problems · Express what we don't know as a variable · Create an equation based on the information provided · Solve for the

How To Solve Word Problems With Multiple Ages? · Sally is 3 times as old as John. · Kim is 6 years more than twice Timothy's age. · Leah is 2 less than 3 times

Objective: Solve age problems by creating and solving a linear equa- tion. An application of linear equations is what are called age problems. When we are.

This math tutorial video explains how to solve age word problems in Algebra given the past, present, and future ages of individuals relative

TabletClass Math:https://tcmathacademy.com/ Math help with algebra word problem involving age. For more math help to include math lessons

If you add up the digits of the number you are trying to divide by 3, and the sum of the digits is divisible by 3, the entire number is divisible by 3. With