Oldest and youngest
Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
Age
14 to 16
Challenge level
Problem
Edith had nine children at regular intervals of $15$ months.
If the oldest is now six times as old as the youngest, how old is the youngest child?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 24 months, or 2 years
$1\underbrace{ \stackrel{\mathrm{15 months}}{\longleftrightarrow}2\stackrel{\mathrm{15 months}}{\longleftrightarrow}3\stackrel{\mathrm{15 months}}{\longleftrightarrow}4 \quad... \quad\stackrel{\mathrm{15 months}}{\longleftrightarrow}}_{\text{8 intervals}}9$
youngest age + 8 $\times$ 15 months = oldest age
= 6 $\times$ youngest age
$\therefore$ 8 $\times$ 15 months = 5 $\times$ youngest age
$\Rightarrow$ 24 months = youngest age