Question

no5 Diana and Becky were on the samesoccer team and took turns being thegoalie. They stopped 9 out of every10 shots made against them. If theother team scored 3 points, how manyballs did Diana and Becky stop fromgoing into the net?balls

Answer 1

ANSWER

27 balls

EXPLANATION

The points scored by the other team are the number of balls Diana and Becky didn't stop.

We know that if the other team would make 10 attempts of goal, only 1 would result in a point. The ratio of scored points to stopped balls is 1:9

Let x be the number of balls they stopped in this match. The other team scored 3 points, so the ratio is 3:x. We know that the ratio should be constant, which means,

$\frac{1}{9}=\frac{3}{x}$

To solve this, we have to multiply both sides by x. On the right side, the x cancels out,

$\begin{gathered} \frac{1}{9}x=\frac{3x}{x} \\ \frac{1}{9}x=3 \end{gathered}$

And then multiply both sides by 9,

$\begin{gathered} \frac{1}{9}\cdot9x=3\cdot9 \\ x=27 \end{gathered}$

Hence, Diana and Becky stopped 27 balls.