Question

Ollie earns a fixed amount of $2,700 per month and a commission of 12% on all of his sales for the month. To cover all of his expenses, he needs to earn at least $5,400 each month.

Part A

Write an inequality that will represent the amount of sales Ollie will need in order to cover his monthly expenses.

Part B

Find the solution and describe what the graph would look like on a number line. Show your work.

Answer 1

Part A)
`0.12x+2,700\geq 5,400`

Part B) see the explanation

Explanation:

Part A) Write an inequality that will represent the amount of sales Ollie will need in order to cover his monthly expenses

Let

x ----> the amount of sales monthly

Remember that

`12\%=12/100=0.12`

we know that

The fixed amount of $2,700 plus the commission of 12% on all of his sales for the month must be greater than or equal to $5,400

so

The inequality that represent this problem is

`0.12x+2,700\geq 5,400`

Part B) Find the solution and describe what the graph would look like on a number line

we have

`0.12x+2,700\geq 5,400`

Solve for x

subtract 2,700 both sides

`0.12x \geq 5,400-2,700\\0.12x \geq 2,700`

Divide by 0.12 both sides

`x\geq \$22,500`

The minimum amount of sales needed to cover his monthly expenses is $22,500

In a number line the solution is the shaded area at right of x=22,500 (closed circle)

see the attached figure to better understand the problem