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#