Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Brooke and Jack have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Brooke earns a base wage of $\$15$ per hour, as well as $\$3$ for every subscription that she sells. Jack gets $\$4$ per subscription sold, in addition to a base wage of $\$4$ 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? $\newline$ Brooke and Jack will each earn $\$\_\_\_\_$ if they sell $\_\_\_$ subscriptions in an hour.

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Solve a system of equations using substitution: word problems

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

\newline

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

\$15

per hour, as well as

\$3

for every subscription that she sells. Jack gets

\$4

per subscription sold, in addition to a base wage of

\$4

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

Brooke and Jack 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 both Brooke and Jack in an hour. $\newline$ Let $y$ be the total amount earned by both Brooke and Jack. $\newline$ Brooke's earnings can be represented by the equation $y = 15 + 3x$ (base wage plus commission per subscription). $\newline$ Jack's earnings can be represented by the equation $y = 4x + 4$ (commission per subscription plus base wage).
Set up equations: Set up the system of equations based on the given information. $\newline$ Brooke's earnings equation: $y = 15 + 3x$ $\newline$ Jack's earnings equation: $y = 4x + 4$
Substitution to solve: Use substitution to solve for $x$ . Since both equations equal $y$ , we can set them equal to each other: $15 + 3x = 4x + 4$
Solve for x: Solve for x. $\newline$ Subtract $3x$ from both sides: $\newline$ $15 + 3x - 3x = 4x + 4 - 3x$ $\newline$ $15 = x + 4$ $\newline$ Now, subtract $4$ from both sides: $\newline$ $15 - 4 = x + 4 - 4$ $\newline$ $11 = x$
Solve for y: Use the value of $x$ to solve for $y$ . $\newline$ We can substitute $x$ into either Brooke's or Jack's earnings equation. Let's use Brooke's: $\newline$ $y = 15 + 3x$ $\newline$ $y = 15 + 3(11)$ $\newline$ $y = 15 + 33$ $\newline$ $y = 48$
Check solution: Check the solution by substituting $x$ into Jack's earnings equation. $\newline$ $y = 4x + 4$ $\newline$ $y = 4(11) + 4$ $\newline$ $y = 44 + 4$ $\newline$ $y = 48$ $\newline$ Since the value of $y$ is the same for both Brooke's and Jack's equations, the solution is correct.