SOLUTION: your math instructor tells you that next weeks test is worth 100 points and contains 29 problems. Each problem is worth either 5 points or 2 points. Because you are studying system

Question 191032: your math instructor tells you that next weeks test is worth 100 points and contains 29 problems. Each problem is worth either 5 points or 2 points. Because you are studying systems of linear equations, your teacher says that for extra credit, you should be able to figure out how much problems of each value are on the test. How many 5 point questions are there? How many 2 point questions are there?
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!

We let x = problems worth 5 points
Also, y = problems worth 2 points

*Hint: There are 29 problems.

It follows, x + y =29, (EQN 1)

*Note:
For every x problem worth 5 points = "5x", plus for every y problem worth 2 points = "2y" equals 100 points:

It follows, 5x + 2y =100pts, (EQN 2)

In EQN 1 we get, x = 29 - y becomes EQN 3 & subst. to EQN 2:

Arrange similar terms: (change sign)

---->
y = 15 , number of problems for 2 points.

Also, via EQN 3:

x = 14, number of problem for 5 points.

Check via EQN 2:

Thank you,
Jojo
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