Question

The Bright Star Video Club offers the two membership plans described below.

Plan A: $50 yearly membership fee and $2 for each video rental
Plan B: $10 yearly membership fee and $4 for each video rental
Greg is planning to enroll in one of these plans. For how many video rentals would the total cost of Plan A be equal to the total cost of Plan B?
A. 50
B. 20
C. 30
D. 40

Answer 1

you can either graph the following equations,
Plan A: y=2x+50
Plan B: y=4x+10
and see where they intersect, and that will give you the answer.
OR
You can substitute each answer for x, like this,
A. 50
Plan A:
y=2(50)+50
y=100+50
y=150
Plan B:
y=4x+10
y=4(50)+10
y=200+10
y=210
So, therefore, A.50 is not the answer.
B.20
Plan A:
y=2x+50
y=2(20)+50
y=40+50
y=90
Plan B:
y=4x+10
y=4(20)+10
y=80+10
y=90
So, B.20 is correct but always check the rest of the answers. Just in case
C.30
Plan A:
y=2x+50
y=2(30)+50
y=60+50
y=110
Plan B:
y=4x+10
y=4(30)+10
y=120+10
y=130
So, C.30 is incorrect.
D.40
Plan A:
y=2x+50
y=2(40)+50
y=80+50
y=130
Plan B:
y=4x+10
y=4(40)+10
y=160+10
y=170
So, in conclusion the correct answer is B.20.

Answer 2

To solve this, you need to create two separate equations and set them equal to each other.

Plan A: y = 2x + 50
Plan B: y = 4x + 10

2x + 50 = 4x + 10

Now solve the combined equation.

2x + 50 = 4x + 10
- 10 - 10
2x + 40 = 4x
-2x -2x
40 = 2x
x = 20