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Question

In basketball, a free throw is worth 1 point and a
field goal is ether 2 points or 3 points.
In the 2016 – 2017 regular season, Stephen
Curry scored 1,999 points. The total number of
2-point and 3-point field goals he made was 675
and the total number of free throws he made
was 325. How many 2-point field goals
and 3-point field goals did Stephen
Curry make in the 2016 – 2017
season?
Define the variables in the problem. Write the
system of equations for the situation. Then solve
using any algebraic method.

Answer 1

Curry scored 1999 points, of which 325 came on free throws.  So Curry scored 1674 points (1999-325) on field goals.

Let's say Curry made x 2-point field goals.  Then he made (675-x) 3-point field goals.

2x + 3 (675-x) = 1674

 

2x + 2025 - 3x = 1674

 

x = 351

So Curry made 351 2-point fields goals and 324 (675-351) 3-point goals.

Check:  351*2 + 324*3 = 702 + 972 = 1674