Question

during a basketball game, your team scored three times as many 2-point field goals than it did 3-point field goals, and scored a total of 90 points. How many field goals did your team score? (there were no 1-point free throws)

Answer 1

Ok, let's define the notation:

A is the number of 2-point field goals that your team scored.

B is the number of 3-point field goals that your team scored:

We know that:

" your team scored three times as many 2-point field goals than it did 3-point field goals,"

This can be written as:

A = 3*B

" And scored a total of 90 points."

A*2 + B*3 = 90

Then we have a system of two equations and two variables:

A = 3*B

A*2 + B*3 = 90

Now we can replace the first equation into the second one and get:

(3*B)*2 + B*3 = 90

B*6 + B*3 = 90

B*9 = 90

B = 90/9 = 10

And we know that:

A = 3*B

A = 3*10 = 30

Then your team scored 30 2-point field goals and 10 3-point field goals (a total of 40 if you combine them)