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?

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Answer 1 · 2016-11-20T17:37:36

She made 4 two-point shots.

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:

$(2 xx t) + (1 xx f) = 13$

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.

$(2 xx t) + (1 xx (9 - t)) = 13$

$2t + 9 - t = 13$

$t + 9 = 13$

$t + 9 - 9 = 13 - 9$

$t = 4$