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# word problem

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You took a test. The test was worth 114 points. There were 30 questions on the test. If questions were worth either 2 or 5 points each, how many 2-point questions were there on the test? How many 5-point questions were on the test?

Mar 28, 2021

### 2+0 Answers

#1
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We can set up we have 2 variables for this problem.

x = # of 5 point questions

y = # of 2 point questions

Since we have 2 variables, we need 2 equations, and we have those equations.

We know that...

\(x + y = 30\)

\(5x + 2y = 114\)

To solve, we first have to make it a one variable equation.

Since \(x = 30 - y\), we can replace all of the \(y\) with \(30 - x\).

So \(5x + 2y = 114\) changes to \(5x + 2(30-x) = 114\)

\(5x + 2(30-x) = 114\)

\(5x + 60 - 2x = 114\)

\(3x + 60 = 114\)

\(3x = 54\)

\(x = 18\)

So...

\(y = 12\)

Your answer is...

There are 18 5 point questions and 12 2 point questions.

And you are done! :)

Mar 28, 2021
#2
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x = 5 pt questions

30 -x   =  2 point questions

5x   +    2 ( 30 - x) = 114

3x = 54

x = 18     5-pointers     then  12     2-pointers

Mar 28, 2021