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

15 shots

Step-by-step 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} (1)/(2)(x\text{ + 5) = 5 + }(1)/(3)x \\ \text{Expand and collect like terms:} \\ (1)/(2)x\text{ + }(5)/(2)\text{ = 5 + }(1)/(3)x \\ (1)/(2)x\text{ - }(1)/(3)x\text{ = 5 - }(5)/(2) \\ \Rightarrow\text{ }(1)/(6)x\text{ = }(5)/(2) \\ \text{Multiply both sides by 6:} \\ x\text{ = }(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.