Question

Klay is playing basketball and has currently made 1/3 of his attempted shots. If he makes his next 5 shots, he will improve his shooting percentage to 50%. How many shots had Klay attempted when he was at a 1/3 success rate?

Answer 1

ANSWER

15 shots

EXPLANATION

Klay has made 1/3 of his attempted shots.

Let the number of attempted shots be x.

This means that he has made:

1/3 * x = x/3

If he makes his next 5 shots, his shooting percentage will increase to 50%. In other words, he will have made half hsi attempted shots.

Adding 5 shots to the shots he already attempted before is:

x + 5

So, now, he would have made:

1/2 * (x + 5)

This is the same as adding the number of shots he had made before to the number of shots he has made now. That is:

$\begin{gathered} \frac{1}{2}(x\text{ + 5) = 5 + }\frac{1}{3}x \\ \text{Expand and collect like terms:} \\ \frac{1}{2}x\text{ + }\frac{5}{2}\text{ = 5 + }\frac{1}{3}x \\ \frac{1}{2}x\text{ - }\frac{1}{3}x\text{ = 5 - }\frac{5}{2} \\ \Rightarrow\text{ }\frac{1}{6}x\text{ = }\frac{5}{2} \\ \text{Multiply both sides by 6:} \\ x\text{ = }\frac{5}{2}\cdot\text{ 6} \\ x\text{ = 15} \end{gathered}$

This means that he had attempted 15 shots when he was at 1/3 success rate.