Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Shelley and Cameron have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Shelley earns a base wage of $\$8$ per hour, as well as $\$3$ for every subscription that she sells. Cameron gets $\$4$ per subscription sold, in addition to a base wage of $\$6$ 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? $\newline$ Shelley and Cameron will each earn $\$\_\_\_\_$ if they sell $\_\_\_$ subscriptions in an hour.

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using substitution: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Shelley and Cameron have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Shelley earns a base wage of

\$8

per hour, as well as

\$3

for every subscription that she sells. Cameron gets

\$4

per subscription sold, in addition to a base wage of

\$6

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?

\newline

Shelley and Cameron will each earn

\$\_\_\_\_

if they sell

\_\_\_

subscriptions in an hour.

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of subscriptions sold by Shelley and Cameron in an hour. $\newline$ Let $y$ be the amount that Shelley and Cameron each earn in that hour. $\newline$ Shelley's earnings can be represented by the equation: $\newline$ $y = 8 + 3x$ (base wage of $\$8$ plus $\$3$ per subscription)
Shelley's Earnings: Cameron's earnings can be represented by the equation: $\newline$ y = $6 + 4x$ (base wage of $\$6$ plus $\$4$ per subscription)
Cameron's Earnings: Now we have a system of two equations: $\newline$ $1$ ) $y = 8 + 3x$ $\newline$ $2$ ) $y = 6 + 4x$ $\newline$ We can use substitution to solve for $x$ by setting the two expressions for $y$ equal to each other: $\newline$ $8 + 3x = 6 + 4x$
System of Equations: Subtract $3x$ from both sides to get: $\newline$ $8 = 6 + x$
Substitution: Subtract $6$ from both sides to solve for $x$ : $\newline$ $x = 8 - 6$ $\newline$ $x = 2$
Solve for x: Now that we have the value of $x$ , we can substitute it back into either equation to find $y$ . Let's use the first equation: $\newline$ $y = 8 + 3x$ $\newline$ $y = 8 + 3(2)$
Substitute Back: Calculate the value of $y$ : $y = 8 + 6$ $y = 14$
Calculate $y$ : Shelley and Cameron will each earn $\$14$ if they sell $2$ subscriptions in an hour.