a test contains 35 questions worth a total of 100 points. there are seven point questions and two point questions. how many two point questions are there how many seven point questions?

Answer 1

These types of word problems create two different equations: 1 for the number of questions and one for the score.

Looking at the number of questions first: There are 7-point questions (we will call "S") and there are 2-point questions (we will call "T") and since all of the questions are either 7-oint or 2-point, then the number of 7-point question and the number of 2-point questions must add up to 35, because there are 35 questions on the test. This, algebraically is:

S + T = 35

Now we look at the points. Each 7-point question contributes 7 points toward the total number of points (which is 100) and each 2-point question contributes 2 points toward the total. So algebraically that is:

7S + 2T = 100

This is the system of equation that must be solved.

S + T = 35

7S + 2T = 100

Multiply top equation by -2.

-2S + -2T = -70

7S + 2T = 100

Add vertically and the "T"s cancel out, leaving

5S = 30

Divide both sides by 5

S = 6 So there are six 7-point questions

Substitute "6" in for "S" in the equation: S + T = 35

6 + T = 35

Subtract 6 from both sides and find that

T = 29 So there are twenty-nine 2-point questions.

CHECK: Does S + T = 35? (6 + 29 = 35? YES, so works in top equation)

Does 7S+2T=100? (7(6) + 2(29) = 42 + 58 = 100? YES so works in bottom equation)

So we have found the correct solution. :-)