I am giving you a test worth 100 points containing 40 questions. There are two points in four point questions on the test. How many of each type a question are on the test?

Answer 1

Let's let x represent the number of 2- point questions and y represent the number of 4- point questions.

Since there are a of 40 questions , we can write:

x + y = 40

Also, since the test is worth 100 points, we can write:

2x + 4y = 100

We can solve these two equations with two unknowns using substitution. Using the first equation , we can write that x = 40 - y

We can substitute this into the second equation for x and write:

2 (40 - y) + 4y = 100

Then using the distributive property, inverse operations, and combining like terms , we cam solve for y or the number of 4-point questions.

80 - 2y + 4y = 100

Combine like terms:

80 +2y = 100

Subtract 80 from both sides of the equation:

80 + 2y - 80 = 100 - 80

2y = 20

Divide both sides of the equation by 2:

2y/2 = 20/2

Then y = 10 questions

There are 10 four-point questions. If there are 10 four -point questions, then there will be 30 two-point questions.