Question

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

There are___five-point problems.
There are___two-point problems.

Answer 1

Answer:

Step One: Since the total number of points is 38, we can create the Let Statements:

Let x= one type of question

Let 38-x= the other type of questions

Step Two: Create an equation to relate the number of questions to the price

100=5x+2(38-x) Distribute

100=5x+76-2x Subtract 76 from both sides of the equation

100-76=5x-2x Combine like terms

24=3x Divide both sides by 3

8=x

∴There are eight questions of one type and 30 questions of the other type.

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Answer 2

Answer:

Let the 2-points no. of question be x

and 5-points no. of question be 38-x

value of 2-points question=2x

and value of 5-points question

=5 (38-x)=190-5x

Total value of question=100

2x+190-5x =100

-3x=100-190

-3x=-90

x=30

Thus, the 2-points no. of questions is (x) 30

and the 5-points no. of questions is (38-30)=8

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