Question

An exam worth 145
points contains 50
questions. Some of the
questions are worth two
points and some are worth

five points. How many two-
point questions are on the

test? How many five-point
questions are on the test?
Write a linear system of
equations that can be used
to solve this problem.

Answer 1

number of 2 pointers --- x
number of 3 pointers ---- y

x + y = 50 or y = 50-x
2x + 3y = 145

use substitution:
2x + 3y = 145
2x + 3(50-x) = 145
2x + 150 - 3x = 145
-x = -5
x = 5

so 5 two-pointers and 45 three-pointers

check:
5+45 = 50, the count checks
2(5) + 3(45) = 10 + 135 = 145 , the total value checks

All is good!