How to solve age word problems with algebra

In an age problem, the same person might show up at two different times. It helps to write down everyone’s age now and at the other time before we turn the relationships into equations.

Compare one person’s current and future age

In $18$ years, Sasha will be four times as old as she is now. Let $s$ be Sasha’s age now. In $18$ years her age is $s + 18$ , and the problem gives us a second way to write that same age, $4 s$ .

Sasha’s age at each time
When	Age
Now	$s$
In 18 years	$s + 18 = 4 s$

\begin{array}{l} s + 18 = 4 s \\ 18 = 3 s \\ s = 6 \end{array}

Sasha is $6$ years old now. In $18$ years she’ll be $24$ , which is four times $6$ .

Write two equations for two people

April is $12$ years older than Eric. In $5$ years, April will be twice as old as Eric. Let $A$ and $E$ be their ages now. Add $5$ to each age to fill in the second row.

Eric’s and April’s ages
When	Eric	April
Now	$E$	$A$
In 5 years	$E + 5$	$A + 5$

Right now $A = E + 12$ . In five years, April’s age is twice Eric’s age at that time, so $A + 5 = 2 (E + 5)$ . Substitute $E + 12$ for $A$ in the second equation.

\begin{array}{l} (E + 12) + 5 = 2 (E + 5) \\ E + 17 = 2 E + 10 \\ E = 7 \end{array}

Then $A = 7 + 12 = 19$ . Eric is $7$ and April is $19$ now. In five years they’ll be $12$ and $24$ , so both relationships in the problem check out.

Learn mathKrista KingOctober 22, 2020math, learn online, online course, online math, algebra, algebra 2, algebra ii, word problems, age word problems, systems of equations, solving systems, solving systems of equations, age problems

How to solve age word problems with algebra

Compare one person’s current and future age

Write two equations for two people

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