Question

Alyssa scored 54 points in her basketball game. If she made 24 shots, how many

of her shots were 2-pointers, and how many were 3-pointers

Answer 1

Alyssa made 18 two-point shots and 6 three-point shots.

Explanation:

From the information given in the problem, we can make two different equations and use substitution to solve the system of equations. Since we know that Alyssa scored 54 points in her game, then the addition of her two-point and three-point shots would be 54, or: 2x + 3y = 54 where 'x' is the number of two-point shots and 'y' is the number of three-point shots. We also know that Alyssa made 24 shots total, so: x + y = 24. Using inverse operations, we can solve for 'y' in the second equation to get: y = 24 - x. We can then substitute this expression into the first equation to solve for 'x':

2x + 3(24 - x) = 54 or 2x + 72 - 3x = 54 or -1x = -18 or x = 18

Since Alyssa made 18 two-point shots out of 24 total shots, then she had to have made 6 three-point shots.