In a basketball game, Jeff scored a total of 36 points. Of the shots he made, 20% were worth three points each, 40% were worth two points each and 40% were worth one point each. How many shots worth one point did Jeff make?

hatchet288
Jun 2, 2018

#1**+1 **

**In a basketball game, Jeff scored a total of 36 points. Of the shots he made, 20% were worth three points each, 40% were worth two points each and 40% were worth one point each. How many shots worth one point did Jeff make?**

Let x be the number of shots he makes for 3 pointers, 2 pointers, and 1 pointers.

So, we have 20%(3x)+40%(2x)+40%(x)=\(\frac{3}{5}x+\frac{4}{5}x+\frac{2}{5}x=36\)

Then, we get: \(\frac{9}{5}x=36\)

And, \(x=36*\frac{5}{9}, x=20\)

Since the question is asking for the number of shots worth 1 point, we can do: \(\frac{2}{5}*20=\boxed{8}\) shots.

tertre
Jun 2, 2018

#2**+1 **

Thanks, tertre....here's another approach

Let x be the number of 3 point shots, y be the number of 2 point shots and z be the number of 1 point shots

So....we have this system

3x + 2y + z = 36 (1)

y = z (2)

2x = z ⇒ x = z/ 2 (3)

Sub (2) amd (3) into (1)

3(z/2) + 2z + z = 36 simplify

(3/2)z + 3z = 36 multiply through by 2

3z + 6z = 72

9z = 72 divide both sides by 9

z = 8 ⇒ he scored 8 one point shots

CPhill
Jun 2, 2018