Question

A basketball player has made24 points out of30 free throws. She hopes to make all her next free throws until her free-throw percentage is or better. How many consecutive free throws will she have to make

Short answer

The required attempts are,$10$ .

Step-by-step solution

Step 1. Given information.

Player made24 points out of30 free throws.

Percentage has to be$=85$ or better.

Step 2. Concept used.

Ratio of two numbers is a quotient when a number is divided by other.

Let n be the total number of free throws required.

After n more attempts, then total throws$=30+n$

Player made points$=24+n$

Step 3. Now, find the total number of attempts so that the free through percentage is  85 or better.

$\begin{array}{c}\frac{24+n}{30+n}=\frac{85}{100}\\ 100(24+n)=85(30+n)\\ 2400+100n=2550+85n\end{array}$

Step 4. Simplify the above equation, to find the value of n.

$\begin{array}{c}2400+100n=2550+85n\\ 100n-85n=2550-2400\\ 15n=150\\ n=10\end{array}$

Therefore, the required attempts are 10.