Question

Solve the problem. In a basketball game, Will scored 33 points, consisting only of three-point shots and two-point shots. He made a total of 15 shots. How many shots of each type did he make? Group of answer choices Two-point shots: 11; three-point shots: 4 Two-point shots: 3; three-point shots: 12 Two-point shots: 12; three-point shots: 3 Two-point shots: 13; three-point shots: 2

Answer 1

To solve for the number of two-point and three-point shots Will made, we can set up a system of equations representing points and shots. Solving the system, we find that Will made 12 two-point shots and 3 three-point shots.

Step-by-step explanation:

The question requires solving a system of linear equations to find out how many two-point and three-point shots Will made to score 33 points in total, having shot 15 times. Let's denote the number of two-point shots he made as x and the number of three-point shots as y. The two equations to represent the scenario are:

1. The total number of points equation: 2x + 3y = 33

2. The total number of shots equation: x + y = 15

Now we solve the system of equations. We can use the second equation to express y in terms of x, which gives us y = 15 - x. Substituting this into the first equation, we have 2x + 3(15 - x) = 33, which simplifies to 2x + 45 - 3x = 33.

Further simplification gives us x = 45 - 33 which results in x = 12. By substituting x = 12 back into y = 15 - x, we get y = 15 - 12, so y = 3.

Therefore, Will made 12 two-point shots and 3 three-point shots to achieve the total of 33 points in the basketball game.