Answer:
a) [tex]\frac{12+n}{15+n}=0.85[/tex]
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 :
[tex]\frac{12}{15}=0.8[/tex]
[tex](0.8).(100)=80[/tex] %
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 :
[tex]\frac{12+n}{15+n}=0.85[/tex] (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) [tex]\frac{12+n}{15+n}=0.85[/tex]
b) Now we need to solve the equation (I) :
[tex]\frac{12+n}{15+n}=0.85[/tex] ⇒
[tex]12+n=(15+n).(0.85)[/tex] ⇒
[tex]12+n=12.75+0.85n[/tex] ⇒
[tex]0.15n=0.75[/tex] ⇒ [tex]n=\frac{0.75}{0.15}=5[/tex]
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) ⇒
[tex]\frac{12+5}{15+5}=0.85[/tex] ⇒ [tex]\frac{17}{20}=0.85[/tex] ⇒ [tex]0.85=0.85[/tex]
