Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Brendan and Kiera have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Brendan earns a base wage of $\$15$ per hour, as well as $\$1$ for every subscription that he sells. Kiera gets $\$3$ 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? $\newline$ Brendan and Kiera 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

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

\$15

per hour, as well as

\$1

for every subscription that he sells. Kiera gets

\$3

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?

\newline

Brendan and Kiera 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 Brendan and Kiera in an hour. $\newline$ Let $y$ be the amount of money that Brendan and Kiera each earn in an hour. $\newline$ We can write two equations to represent the situation: $\newline$ For Brendan: $y = 15 + x$ (since he earns $\$15$ per hour plus $\$1$ for every subscription) $\newline$ For Kiera: $y = 3x + 3$ (since she earns $\$3$ per hour plus $\$3$ for every subscription) $\newline$ The system of equations is: $\newline$ $1$ ) $y = 15 + x$ $\newline$ $2$ ) $y = 3x + 3$ $\newline$ We will solve this system using substitution.
Write Equations: First, we will solve equation $1$ ) for $x$ : $x = y - 15$
Solve Equation $1$ : Next, we substitute $x$ in equation $2$ ) with the expression we found from equation $1$ : $y = 3(y - 15) + 3$
Substitute in Equation $2$ : Now we will solve for $y$ : $y = 3y - 45 + 3$ $y - 3y = -45 + 3$ $-2y = -42$ $y = -42 / -2$ $y = 21$
Solve for y: Now that we have the value for $y$ , we can substitute it back into equation $1$ ) to find $x$ : $x = y - 15$ $x = 21 - 15$ $x = 6$
Substitute in Equation $1$ : We have found that Brendan and Kiera will each earn $\$21$ if they sell $6$ subscriptions in an hour.