To win a basketball game, one team scored 109 points. They made a total of 46 two-pointers and three-pointers. How many of the baskets were worth 2 points, and how many were 3 pointers?

Question

This is systems of 2 equations word problems

Answer 1

Let a = number of 2 point shots

Let b = number of 3 point shots

They made 46 baskets so:

a + b = 46 .... Equation 1

The total score was 109:

2a + 3b = 109 ... Equation 1

In equation 1 solve for a in terms of b:

a = 46 - b

Substitute that into equation 2 and solve for b:

2(46-b) + 3b = 109

92 - 2b + 3b = 109

92 + b = 109

b = 109 - 92

b = 17

a = 46 - b

a = 46 - 17

a = 29

They made 29 two point shots and 17 three point shots