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

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

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.