Question

Stella would like to earn at least $120 per month in order to save up for her College tuition. She babysits for $5 per hour and works at an ice-cream shop for $8 per hour. Stella cannot work more than a total of 20 hours per month. Letx represent the number of hours Stella babysits and y represent the number of hours Stella works at the ice-cream shop. PartA: Write a system of inequalities to represent this scenario. 1st Equation: 2nd Equation: Part B: Stella babysits for 7 hours this month. What is the minimum number of hours she would have to work at the ice-cream shop to earn at least $120? Give your answer to the nearest whole hour. Hint: Use one of your equations in Part A. A 1 1 2 3 4 56

Answer 1

Stella earn by babysitting is $5x and earn by working at an shop of icecream is $8y.

Part (A)

Stella earn at least $120 means sum of Stella's earning by babysitting and by working at an shop of ice cream is more than or equal to 120. So equation is,

`5x+8y\ge120`

Stella cannot work more than 20 hours. So equation is,

`x+y\leq20`

Part (B)

Substitute 7 for x in the equation

`5x+8y\ge120`

to obtain the value of y.

`\begin{gathered} 5\cdot7+8y\ge120 \\ 35+8y-35\ge120-35 \\ (8y)/(8)\ge(85)/(8) \\ y\ge10.62 \end{gathered}`

So value of y is greater than or equal to 10.62. So nearest whole number for y is 11.

Thus Stella work at least for 11 hours at the ice cream for eaning to be at least $120.