Grow Up Fast
How old will Julie be when her age is equal to the sum of her daughters' ages?
Age
11 to 14
Challenge level
Problem
Julie and her daughters Megan and Zoey have the same birthday.
Today, Julie is 32, Megan is 4 and Zoey is 1.
How old will Julie be when her age is the sum of the ages of Megan and Zoey?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 59
Using the number of years that have passed
| Julie | Megan | Zoey | |
| today | 32 | 4 | 1 |
| in $n$ years | 32 + $n$ | 4 + $n$ | 1 + $n$ |
32 + $n$ = 4 + $n$ + 1 + $n$
= 5 + 2$n$
27 = $n$
In 27 years Julie will be 32 + 27 = 59
Using algebra and Julie's age
Julie's age is $J$
$32-4=28$ so Megan's age is $J-28$
$32-1=31$ so Zoey's age is $J-31$
$$\begin{align}(J-28)+(J-31)&=J\\
\Rightarrow 2J-59&=J\\
\Rightarrow J&=59\end{align}$$ So Julie will be $59$.
Using trial
| Julie | Megan | Zoey | M + Z | |
| 32 | 4 | 1 | ||
| 42 | 14 | 11 | 25 | too small |
| 52 | 24 | 21 | 45 | too small |
| 62 | 34 | 31 | 65 | too big |
| 61 | 33 | 30 | 63 | too big |
| 59 | 31 | 28 | 59 | perfect |
Julie is 59