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Casey made 84 field goals during the basketball season for a total of 183 points. Each field goal was worth either 2 or 3 points. How many 2-point and 3-point field goals did Casey make during the season?

Short Answer

Expert verified

Casey made 69 2-point and 15 3-point field goals.

Step by step solution

01

Step 1. Write equation.

Let xrepresents the 2-point field goals and yrepresents the 3-point field goals, such that

x+y=842x+3y=183

02

Step 2. Multiplication.

Multiply x+y=84by 2 and subtract it from 2x+3y=183.

role="math" localid="1648114568747" 2x+3y−2x+y=183−2842x+3y−2x−2y=15y=15

03

Step 3. Substitution.

Substitute 15 for yinto x+y=84and simplify to find x.

x+15=84x=69

Therefore, Casey made 69 2-point and 15 3-point field goals.

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