# A basketball player scored 9 times during one game. She scored a total of 13 points, two for each two-point shot and one for each free throw How many two-point shots did she make?

Nov 20, 2016

#### Explanation:

Let's call the number of two-point shots she score $t$ and the number of free throws $f$.

Because we know she score 9 times we can write an equation:

$t + f = 9$

if we solve for $f$ we get:

$t + f - t = 9 - t$

$f = 9 - t$

We also know the total points score from these 9 shots was 13 and therefore we can write:

$\left(2 \times t\right) + \left(1 \times f\right) = 13$

From the first equation we can substitute $9 - t$ for $f$ in the second equation and then solve for $t$, the number of two-point shots.

$\left(2 \times t\right) + \left(1 \times \left(9 - t\right)\right) = 13$

$2 t + 9 - t = 13$

$t + 9 = 13$

$t + 9 - 9 = 13 - 9$

$t = 4$