Kyle runs a tennis club. 54 of the members are adults and 31 are children. His aim is that at least 60% the members should be children. Form an inequality to find the smallest number of children that Kyle would still need to recruit achieve his aim. Answer ... children

1. Define the unknown and express the new numbers of children and total members.

Let $x$ be the number of children Kyle still needs to recruit.

New number of children $=31+x$.

New total number of members $=54+31+x=85+x$.

2. Form the inequality representing at least 60% children.

Since at least $60\%$ of the members should be children,
$\frac{31+x}{85+x}\geq \frac{60}{100}.$

3. Solve the inequality and choose the smallest whole number of children.

$\frac{31+x}{85+x}\geq \frac35$
$5(31+x)\geq 3(85+x)$
$155+5x\geq 255+3x$
$2x\geq 100$
$x\geq 50$

So the smallest number of children Kyle still needs to recruit is $50$.