What amount will they both have at the same time

Question

Ted and Stacy have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Ted earns a base wage of $15 per hour, as well as $2 for every subscription that he sells. Stacy gets $4 per subscription sold, in addition to a base wage of $5 per hour. If they each sell a certain number of subscriptions in an hour, they will end up earning the same amount. How much would each one earn?

Answer 1

Let's use the variable y to represent the amount of money earned and the variable x to represent the number of subscriptions sold.

We can write an equation for each person that could be used to determine the amount of money earned. Then we can set these two equations equal to one another to find the number of subscriptions each must sell to earn the same amount of money.

For Ted:

y = 2x + 15

For Stacy:

y = 4x + 5

We want to find the point at which both of the y values are equal (in other words, when they would earn the same amount of money):

2x + 15 = 4x + 5

Now solve by combining like terms and using inverse operations:

2x + 15 - 2x = 4x + 5 - 2x

15 = 2x + 5

15 - 5 = 2x + 5 - 5

10 = 2x

10/2 = 2x/2

5 = x

They would each sell 5 subscriptions and each would earn $25.

Ted : y = 2x + 15

25 = 2 • 5 + 15

Stacy: y = 4x + 5

25 = 4 • 5 + 5