Problem 10 · Adults and children on a street
Chained ratios: from $h/d$ and $d/n$ to the count.
Integer answer, at most 4 digitsOn a street live adults ($h$ men and $d$ women) and $n$ children. We know that $h/d = 2/3$, that $d/n = 8$, and that there are 2880 adults in total. How many children are there?
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: from $h/d = 2/3$: for every $3$ women there are $2$ men, i.e. adults come in blocks of $5$.
$$h + d = 2880, \quad h = \tfrac{2}{3}d \;\Longrightarrow\; \tfrac{5}{3}d = 2880 \;\Longrightarrow\; d = 1728, \; h = 1152.$$
And from $d/n = 8$:
$$n = \frac{d}{8} = \frac{1728}{8} = 216.$$
Answer: 216