AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Tristan and Stacy have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Tristan earns a base wage of per hour, as well as for every subscription that he sells. Stacy gets per subscription sold, in addition to a base wage of 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? How many subscriptions would that be?Tristan and Stacy will each earn if they sell subscriptions in an hour.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Tristan and Stacy have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Tristan earns a base wage of per hour, as well as for every subscription that he sells. Stacy gets per subscription sold, in addition to a base wage of 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? How many subscriptions would that be?Tristan and Stacy will each earn if they sell subscriptions in an hour.
- Define Variables: Let's define the variables:Let be the number of subscriptions sold by both Tristan and Stacy in an hour.Let be the amount that each one earns.Tristan's earnings can be represented by the equation:Stacy's earnings can be represented by the equation:Now we have a system of equations:) ) We will use substitution to solve for .
- Earnings Equations: Since both equations equal , we can set them equal to each other:Now we will solve for :Tristan and Stacy will each sell subscriptions in an hour.
- Solve for x: Now we will substitute back into one of the original equations to find , the amount each one earns. We can use Tristan's equation:Tristan and Stacy will each earn if they sell subscriptions in an hour.
