Question

the basketball team scored 82 points from 2 - point and 3 - point baskets. they make 38 baskets altogether. let a represent the number of 2 - point baskets, and let b represent the number of 3 - point baskets.
6 fill in the blank 1 point
c. the team scored type your answer... 2 - point baskets and type your answer... 3 - point baskets.

Explanation:

Step1: Set up the equations

We have two equations based on the problem:

1. The total number of baskets: \(a + b = 38\) (since the total number of 2 - point and 3 - point baskets is 38)
2. The total number of points: \(2a+3b = 82\) (since each 2 - point basket is 2 points and each 3 - point basket is 3 points, and the total points is 82)

From the first equation, we can express \(a\) in terms of \(b\) as \(a=38 - b\)

Step2: Substitute and solve for b

Substitute \(a = 38 - b\) into the second equation:
\[

$$\begin{align*} 2(38 - b)+3b&=82\\ 76-2b + 3b&=82\\ 76 + b&=82\\ b&=82 - 76\\ b&=6 \end{align*}$$

\]

Step3: Solve for a

Substitute \(b = 6\) into \(a=38 - b\):
\(a=38 - 6=32\)

Answer:

The team scored \(\boldsymbol{32}\) 2 - point baskets and \(\boldsymbol{6}\) 3 - point baskets.