MoRE Guess and Check / use Algebra

Question

Caron’s free-throw percentage at this point in the season is 0.875. If he makes only 13 of his next 20 free throws, his percentage will drop to 0.86. How many free throws has Caron made this season so far? Note: a free-throw percentage is calculated by the ratio of successful throws to attempted throws (as a fraction) where the decimal simplification is the number given. For example, if you attempt 15 throws and make only 3 of them, your free-throw percentage would be calculated as 3 15 = 0.20. 

                 So I'm trying to see if I'm even close to the right direction. Sorry, I'm trying to study for an exam and this section baffles me! So far comparing my answers to the answers here, I seem to be close at least.  Thank you in advance for your idea!

Answer 1

Let x=number of free throws that Caron has made so far.

Out of these, 0.875x were successful. If we add 13 to this we get 13+0.875x as the total number of successful throws in x+20 free throws, so the fraction is (13+0.875x)/(x+20)=0.86.

So, 13+0.875x=0.86(x+20)=0.86x+17.2.

(0.875-0.86)x=17.2-13=4.2. And 0.015x=4.2, so x=4.2/0.015=4200/15=280.

So far, then, Caron has had 280 free throws, 245 of which were successful. [(245+13)÷(280+20)=258/300=0.86.]