Problem of the week, 3.

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.

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