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

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?

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.