Solving age word problems in Algebra

How to approach age word problems

Age word problems are like number word problems.

You’ll still need to relate sentences in English to mathematical equations to solve for people’s ages. In this lesson we’ll look at how to do that.

One helpful way to organize these types of problems is by making a table.

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Setting up age word problems from the information we’ve been given

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Solving age word problems

Example

In $18$ years Sasha will be $4$ times older than she is now. How old is she now?

Because Sasha will be four times older in $18$ years, we can relate her age now, $s$ to her age in $18$ years as $4s$.

So we can write the equation $s+18=4s$.

We can also organize the information by making a table.

Now solve for $s$ in the equation.

$s+18=4s$

$s-s+18=4s-s$

$18=3s$

$6=s$

Sasha is $6$ now and in $18$ years she’ll be $4(6)$ or $24$ years old.

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Let’s do an example with more than one person.

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One helpful way to organize these types of problems is by making a table.

Example

April is $12$ years older than Eric. In five years, April will be twice as old as Eric. How old are Eric and April?

Because April is $12$ years older than Eric, we can write

$A=E+12$

Because April will be twice as old as Eric in five years, we need to double Eric’s age in $5$ years to get April’s age in five years. The next equation is

$2(E+5)=A+5$

This is a table that summarizes their ages and our equations:

Now you can substitute $E+12$ for $A$ into $2(E+5)=A+5$ and simplify.

$2(E+5)=(E+12)+5$

$2E+10=E+17$

$E=7$

Substitute $E=7$ into $A=E+12$.

$A=7+12$

$A=19$

Right now Eric is $7$ and April is $19$.

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