Problema Solution
basketball team scores 102 points in a combination of 2 point field goals, 2 point field goals and 1 point foul shots. The team made 56 basketsand 18 more 2 point shots than foul shots. how many of each were made
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let
x = the number of 3 point field goals
y = the number of 2 point field goals
z = the number of 1 point foul shots
basketball team scores 102 points
3x + 2y + z = 102
the team made 56 baskets
x + y + z = 56
the team made 18 more 2 point shots than foul shots
y = 18 + z
by solving the system of equations
3x + 2y + z = 102
x + y + z = 56
y = 18 + z
we find
x = 6 three point field goals
y = 34 two point field goals
z = 16 one point foul shots
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