The ratio of the number of soccer balls and volleyballs in a sports shop was 11 : 7. After 126 soccer balls were added and 233 volleyballs were sold, the ratio became 14 : 3. How many volleyballs were there in the shop at first? Answer ... volleyballs

1. Represent the initial numbers using the given ratio

Let the initial number of soccer balls be $11x$ and the initial number of volleyballs be $7x$.

2. Form an equation using the changed quantities and new ratio

After the changes,

soccer balls $=11x+126$,

volleyballs $=7x-233$.

Given the new ratio is $14:3$,
$\frac{11x+126}{7x-233}=\frac{14}{3}.$

3. Solve the equation and find the initial number of volleyballs

$3(11x+126)=14(7x-233)$
$33x+378=98x-3262$
$3640=65x$
$x=56$

Initial number of volleyballs:
$7x=7(56)=392.$