Question

The two top NBA players played a basketball game against the RSM team. Together the NBA players made 85 baskets, scoring one point for free throws and two or three points for field goals. They scored a total of 184 points during the game. If they made 22 free throws, how many three-point field goals did they make?

Answer 1

Answer: 36 three-point field goals.

Step-by-step explanation:

To solve this problem, set up a system of equations. Let's call the number of  one-pointers $w$, the number of two-pointers $x$, and the number of three-pointers $y$. We are trying to find $y$ here. We also know that $w+x+y=85$, because that is the total amount of baskets, and also that $w+2x+3y=184$, which is the total amount of points. We know that there were 22 free throws,  so that means we can take away 22 baskets from the first equation, and also 22 points from the second equation. Now the equations are $x+y=63$ and $2x+3y=184$. Solving the equations using our knowledge of systems of equations, you get that $y=36$. So, 36 is the answer. Let me know if anything was unclear, and I hope this helped.