At a basketball​ game, a team made 56 successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored 94 points in all.

Question

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

Answer 1

Hi,

Let's say that P represents that number of shots worth one point, and K represents the number of shots worth 2 points.

We are told that there were a total of 56 shots, meaning:

P+K=56

We are also told that the total number of points in the game was 94. Therefore, we know that

P+2K=94

The reason there is a 2 in front the K is because those shots are worth two points.

Now we have two equations and two unknowns, so we can solve this problem.

The fastest way to do this is by solving for P in the first equation and plugging it into the second equation.

P=56-K

Plug it into the second equation:

56-K+2K=94

Now solve for K:

K=94-56=38

To solve for P, we plug in the value of K in any of the two initial equations:

P+38=56

P=56-38=18

Hope this helps.