Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
valentina and marshall have summer jobs selling newspaper subscriptions door - to - door, but their compensation plans are different. valentina earns a base wage of $11 per hour, as well as $1 for every subscription that she sells. marshall gets $2 per subscription sold, in addition to a base wage of $3 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?
valentina and marshall will each earn $\square$ if they sell $\square$ subscriptions in an hour.

Explanation:

Step1: Define variables

Let $x$ = number of subscriptions, $y$ = total earnings (in dollars)

Step2: Write Valentina's earnings equation

Valentina's base wage is $11 per hour plus $1 per subscription:
$y = 11 + 1x$

Step3: Write Marshall's earnings equation

Marshall's base wage is $3 per hour plus $2 per subscription:
$y = 3 + 2x$

Step4: Substitute equations to solve for $x$

Set the two expressions for $y$ equal:
$11 + x = 3 + 2x$
Subtract $x$ from both sides:
$11 = 3 + x$
Subtract 3 from both sides:
$x = 11 - 3 = 8$

Step5: Calculate total earnings $y$

Substitute $x=8$ into Valentina's equation:
$y = 11 + 8 = 19$

Answer:

Valentina and Marshall will each earn $\$19$ if they sell 8 subscriptions in an hour.