need help with math question

Question

At a basketball​ game, a team made

52

successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored

86

points in all. Write and solve a system of equations to find the number of each type of shot.

Answer 1

Let's start by defining our variables! We have the number of 1-point shots that were made, which I'll call O, and the number of two-point shots that were made, which I'll call T. We know that the total number of shots made was 52, so O + T = 52. The total score was 86, so 1O + 2T = 86 because each O is worth 1 total point and each T is worth 2 total points. We now isolate the variables so we can solve for them. Let's start by solving for T.

O + T = 52, so O = 52 - T.

O + 2T = 86, so O = 86 - 2T.

We can substitute the value of O in the first equation for the value of O in the second to get:

52 - T = 86 - 2T. Let's solve for T by first adding 2T to each side to get 52 + T = 86. Subtract both sides by 52, and T = 34!

Now we can find O. O = 52 - T, so O = 52 - 34, which means O = 18. The team made 18 one point shots and 34 two point shots.