I cannot figure this out

Question

The Cougars scored a total of 84 points in their basketball game last night against the bears. The cougars made no one-point shots and a total of 38 two-point and three-point shots. How many three-point shots were made and how many two-point shots were made.

Answer 1

To solve problems like this one, you can set up a system of two equations and then solve for one variable at a time. The key step is finding the two equations to solve.

Start by assigning variables to the two numbers we want to know.

x = number of 2 point shots

y = number of 3 point shots

We can find one equation by adding up the total number of shots

(Number of 2 point shots) + (Number of 3 point shots) = (Total shots)

or

x + y = 38

We can find another equation by multiplying the number of each type of shot by their score value,

(2 points)x + (3 points)y = (84 points)

or

2x + 3y = 84

So our system of equations is,

x + y = 38

2x + 3y = 84

Now we can solve the system by whichever method you prefer, I will use the addition method here, however you could also use the substitution method.

2x + 2y = 76 [Multiplying both sides of the first equation by 2]

2x + 3y = 84

Subtracting the second equation by the first, we get,

y = 8

Since y = 8, and x + y = 38, we know

x + 8 = 38

x = 30

So the number of 2 point shots is 30 and the number of 3 point shots is 8.