Savannah is working two summer jobs, making $\$ 10$ per hour washing cars and making $\$18$ per hour tutoring. In a given week, she can work at most $12$ total hours and must earn a minimum of $\$ 160$ . If Savannah worked $7$ hours tutoring, determine all possible values for the number of whole hours washing cars that she must work to meet her requirements. $\newline$ Answer: $\square$

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Grade 7

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Q. Savannah is working two summer jobs, making

\$ 10

per hour washing cars and making

\$18

per hour tutoring. In a given week, she can work at most

12

total hours and must earn a minimum of

\$ 160

. If Savannah worked

7

hours tutoring, determine all possible values for the number of whole hours washing cars that she must work to meet her requirements.

\newline

Answer:

\square

Calculate earnings from tutoring: Calculate the earnings from tutoring. $\newline$ Savannah earns $\$18$ per hour tutoring. If she worked $7$ hours tutoring, her earnings from tutoring would be: $\newline$ Earnings from tutoring = $\$18/\text{hour} \times 7 \text{hours}$ $\newline$ Earnings from tutoring = $\$126$
Calculate minimum remaining amount: Calculate the minimum remaining amount she needs to earn from washing cars. $\newline$ Savannah needs to earn a minimum of $\$160$ in total. She has already earned $\$126$ from tutoring, so she needs to earn at least: $\newline$ Minimum remaining earnings = $\$160 - \$126$ $\newline$ Minimum remaining earnings = $\$34$
Calculate minimum hours washing cars: Calculate the minimum number of hours she needs to work washing cars to earn the remaining amount. $\newline$ Savannah earns $\$10$ per hour washing cars. To find out the minimum number of hours she needs to work to earn $\$34$ , we divide the remaining amount by her hourly wage from washing cars: $\newline$ Minimum hours washing cars = $\frac{\$34}{\$10/\text{hour}}$ $\newline$ Minimum hours washing cars = $3.4$ hours $\newline$ Since she cannot work a fraction of an hour, she needs to work at least $4$ whole hours washing cars.
Check total hours worked: Check the total number of hours worked to ensure it does not exceed the maximum allowed hours. $\newline$ Savannah can work at most $12$ hours in total. She has already worked $7$ hours tutoring. If she works $4$ hours washing cars, the total number of hours worked would be: $\newline$ Total hours worked = $7$ hours tutoring + $4$ hours washing cars $\newline$ Total hours worked = $11$ hours $\newline$ Since $11$ hours is less than or equal to the maximum of $12$ hours, working $4$ hours washing cars is a possible solution.
Determine possible values: Determine if there are any other possible values for the number of whole hours washing cars. $\newline$ Since Savannah has already worked $7$ hours tutoring and can work a maximum of $12$ hours, she can work up to $5$ hours washing cars ( $12$ hours total - $7$ hours tutoring). However, she only needs to work $4$ hours to meet her minimum earnings requirement. Therefore, the possible values for the number of whole hours washing cars are $4$ and $5$ hours.