Question

At a festival 2/7 of number of girls was equal to 3:5 of the number of boys. There were 165 fewer boys than girls, how many children were at the festival in all.

Answer 1

`\boxed{365}`

Explanation:

Let g = number of girls

and b = number of boys

We have conditions (1) and (2):

`\begin{array}{lrcll} & 1650 + 10b & = & 21b & \text{Distributed the 10} \\ & 1650 & = & 11b & \text{Subtracted 10b from each side} \\ (5) & b & = & 150 &\text{Divided each side by 11} \\ & g - 150 & = & 165 & \text{Substituted (5) into (2)} \\ & g & = & 215 &\text{Added 150 to each side} \\\\ & g + b & = & 365 &\text{Added girls and boys} \\\end{array}`

`\text{The number of children at the festival was \boxed{\textbf{365}}}`

Check:

`\begin{array}{rlcrl}(2)/(7)*315& = (3)/(5) *150 & \qquad & 315 - 160 & =165\\90 & = 90& \qquad & 165 & = 165\end{array}`