substitutions in a word problem

Question

a basket ball team scores a total of 160 points.a total of 74 baskets where made. how many 2 point and 3 point goals where made?

Answer 1

We have a number of 2 point shots

and a number of 3 point shots.  The total number of

shots is 74 and the total points is 160

 

Let x = # 2 point shots

Let y = # 3 point shots

 

x + y = 74  _________ eq 1

2x + 3y = 160 _______eq 2

 

multiply equation 1 by -2 and add the equations

 

-2x - 2y = - 148

 2x + 3y =  160

--------------------

         y = 12

 

x + y = 74

x + 12 = 74

x = 62

 

There were 62 of the 2 point shots

and 12 of the 3 point shots

Answer 2

There are three ways to score--free throws, and field goals (either 2 pts each or 3 pts each).

Without knowing how many free throws were made (1 point each), this question cannot be solved.