SOLUTION: On a math test the total number of points possible is 120. There are 44 questions on the test. Questions are worth one point, three points or five points. The number of three poi

Question 1070055: On a math test the total number of points possible is 120. There are 44 questions on the test. Questions are worth one point, three points or five points. The number of three point questions is ten less than twice the number of one point questions. How many five point questions are on the test? (Note: guess and check or a table is not acceptable�must set up and solve algebraically).
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
On a math test the total number of points possible is 120. There are 44 questions on the test. Questions are worth one point, three points or five points. The number of three point questions is ten less than twice the number of one point questions. How many five point questions are on the test?
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Questions Eq:: o + t + f = 44 questions
Points Eq:::: o +3t +5f = 120 points
Relation:: t = 2*o -10
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Rearrange::
o + t + f = 44
o +3t +5f = 120
2o - t +0f = 10
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Use any method you know to solve the system to get:
o = 15 (one pt. questions)
t = 20 (three pt. questions)
f = 9 (five pt. questions)
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Cheers,
Stan H.
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Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
x one-point questions
y of three point each
z of five point each

Account for the total points.

Account for quantity of questions.

Last part of the description:

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You might use any method you are comfortable with. Immediate substitution for y seems like a good way to go; and then simplify the remaining two equations.
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