Question

4. Next week your math teacher is giving a chapter test worth 100 points. The test will consist of 35

problems. Some problems are worth 2 points and some problems are worth 4 points. How many
problems of each value will be on the test?

Answer 1

Explanation:

Let T stand for the number of 2 point questions and F for the number of 4 point questions.

We are told that:

2T + 4F = 100 {The total score is the sum of 2 and 4 point questions times their point values]

and that

T + F = 35 [the total number of questions is 35]

Rearrange the last equation to solve for either T or F, and substitute that into the first equation:

T = 35 - F

--

2T + 4F = 100

2(35-F) + 4F = 100

70 - 2F +4F = 100

2F = 30

F = 15

Since T + F = 35, T = 20

Check:

2-Point Questions: 20*2 = 40

4-Point Questions: 15*4 = 60

Total test is 100 points