Question

Your math instructor tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worth either 5 points or 2 points. Write two linear equations based upon this information and solve the system. How many questions of each value are on the test?

Math Word Problem
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asked 2020-12-09

Your math instructor tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worth either 5 points or 2 points. Write two linear equations based upon this information and solve the system.
How many questions of each value are on the test?

Answers (1)

2020-12-10
Step 1
Let x be the 2 point questions and y be the 5 point questions. Write the equation can be written as the linear equation as given below.
x+y=38...(1)
2x+5y=100...(2)
Multiply equation(1)from equation (2),
2x+2y=76...(3)
Subtract equation(1)from equation(2),
3y=24 \({y}=\frac{24}{{3}}\) (Divide by 3 on both sides)
y=8
Step 2
Substitute 8 for y in equation (1),
x+8=38
x=38-8 (subtract 8 on both sides)
x=30
Thus,there are 30 questions had 2 points and 8 questions had 5 points.
Step 3
Result:
The count of 2 point questions are 30 and 5 point questions are 8.
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