Question

10. The test was worth 100 points. There were 28 problems on the test. Some of the

problems were worth 3 points and others were worth 5 points. How many of each were
there?

Answer 1

20 3-point questions and

8 5-point questions.

Explanation:

Let there be x 3 point problems and y 5 point problems. So we have:

x + y = 28 Multiply this equation by -3:

-3x - 3y = -84

3x + 5y = 100 Adding the last 2 equations:

0 + 2y = 16

y = 8

So x = 28 - 8 = 20.

Answer 2

There are 20 3-point questions and 8 5-point questions

Explanation:

x=3 point y=5 point

x+y=28 ----> x=28-y

3x+5y=100

3(28-y)+5y=100

84-3y+5y=100

84+2y=100

2y=16

y=8

28-8=20