Age Word Problem in Algebra

Age Word Problem in Algebra

Age problems are perfect place to practice algebra.

• The goal is usually to find each person’s current age.

• Instead of using XYZ, let's use A(udrey), C(helsie), C(hleo), C(laudia), J(essie) and so on.

• When solving age problems, generally the age of two different people both now and in the future (or past) are compared.

• Each time point corresponds to one equation. So we have two equations for two variables.

• In algebra, we need to two equations to solve two variables.

Q1. Joey is 20 years younger than Becky. In two years, Becky will be twice as old as Joey.

• Now: J=B-20

• In 2 years, Joey will be J+2 years old. Becky is B+2 years old.

• Becky: 2(J+2)=(B+2)

Solve Two 2-variable equations:

• J=B-20

• 2(J+2)=(B+2)

• Last week we talked about subtracting equations.

• Here we replaced one variable J by Expression B-20.

Open Ended

By plugging J=B-20, 2(J+2)=(B+2) becomes ?

Write down the new equation. (Open poll)

How to solve 2(B-20+2)=B+2?

• Algebra operation

• Try app Algebra Touch, available on iOS Appstore

• Pause here and download Algebra Touch

Learn and Solve Algebra on iPAD!

• Open the "Algebra Touch" App.

• Select "Advanced Distribution" Tab, Scoll down to the bottom "Create Your Own"

• Typing 2*(B-20+2)=B+2. Click Done.

• Play with the equation and solve B=?.

• If you can not solve it, please start from Beginner's Tab and learn some algebra.

Fill in the Blanks

Solve the equation using algebra or the APP.

2*(B-20+2)=B+2

B=?

Q2, Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?

• The first sentence tells us that Carmen is 12 years older than David (this is the current age) : C=D+12

• The underlined 2nd sentence tells us the age change for both Carmen and David is five years ago (−5)

• Write down equation with D being the only unknown for the underlined sentence: "Five years ago, the sum of their ages was 28."

Open Ended

Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?

The first sentence tells us that Carmen is 12 years older than David (this is the current age) : C=D+12

Write down the equations with D being the only unknown for the second sentence that "Five years ago, the sum of their ages was 28."? (open poll)

Fill in the Blanks

Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?

Solve your equation using algebra or the APP. D=?

Q3, The sum of the ages of Nicole and Kristin is 32. In two years, Nicole will be three times as old as Kristin. How old are they now?

• 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 K = 32 − N 

• The second sentence tells us that the age change for both Nicole and Kristen is in two years (+2)

• Write down the equation with N being the only unknown for the underlined sentence "In two years, Nicole will be three times as old as Kristin."

Open Ended

The sum of the ages of Nicole and Kristin is 32. In two years, the sum of the ages of Nicole and Kristin is 32.

Write down the equation with K being the only unknown for the underlined sentence.

Fill in the Blanks

Solve your equation using algebra or the APP. K=?

Q4. Louise is 26 years old. Her daughter Carmen is 4 years old. In how many years will Louise be double her daughter’s age?

• 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 (x)

• Write down the equation for "In x years, Lous will be double her daughter 's age"

Open Ended

Louise is 26 years old. Her daughter Carmen is 4 years old.

Write down the equation for "In x years, Lousie will be double her daughter 's age"

Fill in the Blanks

Louise is 26 years old. Her daughter Carmen is 4 years old.

Solve x for "In x years, Lousie will be double her daughter 's age"

Open Ended

Q5. The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary. Write down the equation with M being the only unknown for the underline sentence. (open poll)

Fill in the Blanks

The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary. Solve M=? (by algebra or APP)

Open Ended

Q6. 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.

Write down equation with S being the only unknown for the underline sentence. (open poll)

Fill in the Blanks

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.

Solve son's age (using algebra or APP)

Open Ended

Q7. Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now?

Write down the Equation with C being the only unkown for the underlined sentence

Fill in the Blanks

Q7. Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now?

Solve C=? (by algebra or the APP)

Open Ended

In January of the year 2000, I am one more eleven times as old as my son Williams, In January of the year 2009, I am seven more than three times old as him. How old was my son in January of 2000?

Write down the equation with S(on) being the only unknown for the underline sentence.

Fill in the Blanks

In January of the year 2000, I am one more eleven times as old as my son Williams, In January of the year 2009, I am seven more than three times old as him. How old was my son in January of 2000?

Solve S(on)=? using algebra or the APP.