Question

A math test is worth 100 points and has 30 problems.

Each problem is worth either 3 points or 4 points.
How many 4-point problems are there?

Answer 1

Explanation:

Let x be the number of problems worth 3 points.

No. of problems worth 4 points = 30 - x

Score of 3-point problems = 3*x = 3x

Score of 4-point problems = 4 *(30-x) = 4*30 - 4*x = 120 - 4x

Total score = 100

3x + 120 -4x = 100

-x +120 = 100

-x = 100 - 120

-x = -20

x = 20

No. of 3-point problems = 20

No.of 4-point problems = 10

Answer 2

Let x = 3 point questions and y = 4 point questions.

x + y = 30 total questions

Rewrite as x = 30 - y

3x + 4y = 100 total points

replace x in the points equation:

3(30-y) +4y = 100

Use distributive property:

90 - 3y + 4y = 100

Combine like terms:

90 + y = 100

Subtract 90 from both sides:

y = 10

There are 10 4 point questions.