Question

So far this basketball season, Sherita made 46 of her

first 60 free throws, giving her a free-throw average of
about 76.7%. What is the minimum number of free
throws she would need to make from now on in order
to have a free-throw average of at least 80% ?

Answer 1

Sherita would need to make 10 free throws

Explanation:

Proportions

Sherita made 46 of her first 60 free throws in this basketball season. Calculating the average we get:

`\displaystyle (46)/(60)=76.7\%`

Sherita wants to have a free throw average of at least 80% in her next x free throws. This means she will have 46+x made throws out of 60+x total throws. For this new performance, the new average would be:

`\displaystyle (46+x)/(60+x)`

And we equate it to 80% (0.8 in decimal):

`\displaystyle (46+x)/(60+x)=0.8`

Multiplying by 60+x:

`46+x=0.8(60+x)`

Operating:

`46+x=48+0.8x`

Subtracting 46 and 0.8x:

0.2x=2

Dividing by 0.2

x = 10

Sherita would need to make 10 free throws