SOLUTION: A basketball team recently scored a total of 81 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots. Altogether, the team made 46 baskets an

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Question 387091: A basketball team recently scored a total of 81 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots. Altogether, the team made 46 baskets and 9 more 2-pointers than foul shots. How many of each shot were made?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

9 more 2-pointers than foul shots, 46 baskets in all   

Let x  and (x+9) represent the number of foul shots and 2-pointers respectively

then 3 pointers would be [46 - x - (x+9))] 0R (37-2x)

Question States***total of 81 points

 1*x + 2*(x+9) + 3*(37-2x) = 81

Solving for x

 1x + 2x+ 18 + 111 -6x = 81

       129 - 3x = 81 

            48 = 3x

            16 = x, the number of foul shots.  

            25 2-pointers,  (16+9)

             5 3-pointers   (46 - 16 - 25)

CHECKING our Answer***

 50 + 15 + 16 = 81 points total