Question

You need to earn at least $1700 in order to afford a special vacation. You've found 2 part-time jobs: painting fences at $12/hr and managing a laundry mat for $18/hr. However, you can only work a maximum 13 hours per week. If x is the number of hours spent painting fences and y is the number of hours spent managing the laundry mat, which of the following system of inequalities best describes your scenario:

Please see the attached photo for the answer options

Answer 1

`12x+18y\geq 1,700`

`x+y\leq 13`

`x\geq 0`

`y\geq 0`

Explanation:

Let

x ----> the number of hours spent painting fences

y ----> the number of hours spent managing the laundry mat

we know that

you can only work a maximum 13 hours per week

so

`x+y\leq 13` ----> inequality A

Remember that the word"at least" means "greater than or equal to"

so

`12x+18y\geq 1,700` ----> inequality B

Remember that the number of hours cannot be a negative number

so

`x\geq 0` ---> inequality C

`y\geq 0` --> inequality D

therefore

The system of inequalities that describe the situation is

`12x+18y\geq 1,700`

`x+y\leq 13`

`x\geq 0`

`y\geq 0`