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?

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

Step-by-step 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

20 3-point questions and

8   5-point questions.

Step-by-step 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.

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