Question

Bobby can work at most 20 hours next week, but she needs to earn at least $150. Herdog-walking job pays her $6 per hour and her iob as a car wash attendant pays her $10 perhour. If d is the number of hours she walks dogs this week and w is the number of hours sheworks at the car wash, write a system of inequalities that represents Bobby's situation.

Answer 1

Let d represent the number of hours Bobby walks dogs,

and w be the number of hours she works at the car wash.

Given that she can work at most 20 hours next week, this implies that the total number of hours she works is expressed as

`d+w\leq20`

If her dog-walking job pays her $6 per hour, this implies that for d number of hours, she will earn

`\begin{gathered} \frac{\$6}{1\text{ hour}}* d\text{ hours} \\ =\$\text{ 6d} \end{gathered}`

and her iob as a car wash attendant pays her $10 per hour, similarly for w number of hours, she will earn

`\begin{gathered} \frac{\$10}{1\text{ hour}}* w\text{ hours} \\ =\$10w \end{gathered}`

Given that she needs to earn at least $150, this implies that her total earnings will be expressed as

`6d+10w\ge150`

Hence, the system of inequalities that represents Bobby's situation is:

`\begin{gathered} d+w\leq20 \\ 6d+10w\ge150 \end{gathered}`