Question

A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?

Answer 1

Answer:

a) $\frac{12+n}{15+n}=0.85$

b) She needs 5 consecutive free throws in order to raise her percent to

85 %

Step-by-step explanation:

We know that a basketball player made 12 out of 15 free throws she attempted.

We can calculate its percent of successful free throws as :

$\frac{12}{15}=0.8$

$(0.8).(100)=80$ %

Now, If she wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85 % we can write :

$\frac{12+n}{15+n}=0.85$ (I)

In the equation (I) ''n'' represents the number of consecutive free throws she must have to raise the percent to 85 %.

We answer

a)  $\frac{12+n}{15+n}=0.85$

b) Now we need to solve the equation (I) :

$\frac{12+n}{15+n}=0.85$ ⇒

$12+n=(15+n).(0.85)$ ⇒

$12+n=12.75+0.85n$ ⇒

$0.15n=0.75$ ⇒ $n=\frac{0.75}{0.15}=5$

We found out that she needs 5 consecutive free throws to raise the percent of successful free throws to 85 %.

We can verify by replacing the value of ''n'' in the equation (I) ⇒

$\frac{12+5}{15+5}=0.85$  ⇒  $\frac{17}{20}=0.85$ ⇒ $0.85=0.85$