How many Shots?

Question

A basketball team recently scored a total of 92 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots. Altogether, the team made 50 baskets and 22 more 2-pointers than foul shots. How many shots of each kind were made

Answer 1

This problem is meant to be a system of equations.
If we let x= # of 3-pointers
y= # of 2-pointers
z= # of 1-pointers

Based upon the above, we get the following system of equations:
<br< 3x + 2y + z = 92
x + y + z = 50
y = z + 22

So, this would be re-stated as the following:

3x + 2y + z =92
x + y + z = 50
y - z = 22

I prefer to have the equations giver me x= on 1st row; y=on 2nd row, and z=on 3rd row

This one is going to require some row interchange to solve and have them in that format. But, it's much cleaner-looking that way!

Now that you've got the setup and the strategy, if you're familiar with executing row operations, then you should be able to finish your work on this problem.