Question

The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test?

Answer 1

i tried doing it but i ended up just confusing myself

Answer 2

so you want to know how many 2 point questions and how many 4 point questions there are. That means that those are your two variables.

Lets say the number of 2 point questions is represented by x
and the number of 4 point questions is represented by y

Now since we have 2 variables, we need to equations to solve for each.

First, we know that the test is a total of 80 points.
You get 2 points for every x question so we'll write that as 2*x
and 4 points for every y question so 4*y
and the total is 80
therefore:
2*x + 4*y = 80

We also know that there is a total of 34 questions.
therefore:
x + y = 34

Your system of 2 equations in 2 variables representing the problem is therefore:

2*x + 4*y = 80
x + y = 34

There are lots of ways of solving from here. Do you know any?

Answer 3

@LifeEngineer method of substitution, method of elimination, and graphing?

Answer 4

i think elimination would do fine for this one

Answer 5

multiply the second equation by -2 and add

Answer 6

x+y=34*-2 ?

Answer 7

-68

Answer 8

2x + 4y = 80
-2x - 2y = -68

Answer 9

add ing these 2 equations will eliminate x

Answer 10

@cwrw238 2x+4y=80+(-2)x-2y=-68?

Answer 11

yes

Answer 12

subtract them term by term to get an equation in y only

Answer 13

@cwrw238 4x+2y=80+(-68)?

Answer 14

no