Question

Lesson 18: Uso Systems of Equations to solve probierns 7. James scored a total of 15 points during a basketball game. During the game, he made only free throws, worth 1 point each, and 3-point baskets. He made a total of 7 baskets. How many free throws and how many 3-point baskets did James make during the game? A. o free throws and 7 three-point baskets B. 1 free throw and 6 three-point baskets C. 2 free throws and 5 three-point baskets D. 3 free throws and 4 three-point baskets

Answer 1

ANSWER

James made 3 free throws and 4 three-point baskets.

EXPLANATION

We want to find the number of free throws and three-point baskets James made.

Let the number of free throws be f.

Let the number of three-point baskets be b.

James made a total of 7 baskets.

This means that:

$f+t=7$

Each free throw is worth 1 point and each three-point basket is worth 3 point.

The total number of points he had is 15 points.

This means that:

$f+3t=15$

We now have a system of simultaneous equations:

$\begin{gathered} f+t=7 \\ f+3t=15 \end{gathered}$

From the first equation:

$f=7-t$

Substitute that into the second equation:

$\begin{gathered} 7-t+3t=15 \\ 7+2t=15 \\ \Rightarrow2t=15-7=8 \\ t=\frac{8}{2} \\ t=4 \end{gathered}$

Substitute that into the equation above:

$\begin{gathered} f=7-4 \\ f=3 \end{gathered}$

Therefore, James made 3 free throws and 4 three-point baskets.