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

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.

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