Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Haley is looking for a job cutting hair. One option is self-employment at The Oakdale Salon, where she would pay $\$642$ per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $\$6$ for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Haley pay? $\newline$ If Haley performed _ haircuts in a month, she would pay $\$$ _ to either salon.

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Grade 8

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

Haley is looking for a job cutting hair. One option is self-employment at The Oakdale Salon, where she would pay

\$642

per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon

\$6

for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Haley pay?

\newline

If Haley performed _____ haircuts in a month, she would pay

\$

_____ to either salon.

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of haircuts Haley performs in a month. $\newline$ Let $y$ be the amount Haley pays to the salon. $\newline$ For The Oakdale Salon, Haley pays a flat rent of $\$642$ , so the equation is: $\newline$ $y = 642$
Substitution Method: To solve the system using substitution, we can substitute the value of $y$ from the first equation into the second equation: $\newline$ $642 = 6x$
Calculate x: Calculate the value of x: $\newline$ $x = 107$
Calculate Total Payment: Now, we need to find out how much Haley would pay to either salon. We can use either equation for this, but since we already have $y = 642$ from the first salon, we know that's the amount she would pay there. For the franchise salon, we can check by multiplying the number of haircuts by the cost per haircut: $y = 6 \times 107$
Calculate Total Payment: Calculate the value of $y$ for the franchise salon: $y = 642$