Challenge Level

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

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 $59$.

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

You can find more short problems, arranged by curriculum topic, in our short problems collection.