Percentage of free-throws made versus number made

[bdelaughter]

A basketball player has made 87.5% of her free-throws. If she only makes 13 of her next 20 free-throws, her percentage will drop to 86%. How many free-throws has she made?

I do not know how to set this word problem up. Thanks for your help.

 

[arthur ohlsten]

let x be the number of free throws.
she has successfully made .875x free throws

if she makes 13 of the next 20 her average =.86
total number of throws=x+20
successful throws = .875x+13
%=number of successes / number of tosses

.86= [.875x+13]/[ x+20]
.86x+17.2=.875x+13
4.2=.015x
x=280 answer
Arthur

 

[soroban]

Re: Percentages of Basket Made

Hello, bdelaughter!

Arthur set it up very nicely and solved,
. . but forgot to answer the question.

A basketball player has made 87.5% of her free-throws.
If she only makes 13 of her next 20 free-throws, her percentage will drop to 86%.
How many free-throws has she made?

Let $\displaystyle x$ = original number of shots taken.

She made $\displaystyle 87.5\%$ of them, so she has made: $\displaystyle \,0.875x$ free-throws.

If she makes 13 more free-throws, she will have made $\displaystyle 0.875x\,+\,13$ free-throws
. . in a total of $\displaystyle x\,+\,20$ shots.

This ratio is 86%: \(\displaystyle \L\:\frac{0.875x\,+\,13}{x\,+\,20} \:=\:\frac{86}{100}\)

Cross-multiply: $\displaystyle \:87.5x\,+\,1300\:=\:86x\,+\,1720\;\;\Rightarrow\;\;1.5x\:=\:420\;\;\Rightarrow\;\;x\:=\:280$

. . She has taken 280 shots already.

Therefore, she has made: $\displaystyle \,\frac{7}{8}\,\times\,280\:=\:\fbox{245}$ free-throws.