Question

Be sure to fully show the system of equations for each problem and the process used to solve the system.You are starting an office-cleaning service. You decide to charge both large and small offices. You charge $55 for a small office and $85 for a large office. You clean 14 offices and make $920. How many small offices and how many large offices did you clean?

Answer 1

Given:

The charge for a small office = $55.

The charge for a large office = $ 85.

The total number of offices = 14.

The total amount = $ 920.

Required:

We need to find a number of small offices and large offices.

Step-by-step explanation:

Let x be the number of the small office and y be the number of the large office.

The equation of the total number of offices.

`x+y=14`

`x=14-y`

The equation of the total amount.

`55x+85y=920`

Substitute x =14-y in the equation.

`55(14-y)+85y=920`

`55*14-55y+85y=920`

`770+30y=920`

Subtract 770 from both sides of the equation.

`770+30y-770=920-770`
`30y=150`

Divide both sides by 30.

`(30y)/(30)=(150)/(30)`
`y=5`
`Substitute\text{ y=5 in the equation x=14-y.}`
`x=14-5`
`x=9`

Final answer:

The equations are

`x+y=14`

`55x+85y=920`

The number of small offices are 9.

The number of large offices are 5.