A local business was looking for a cleaning service to work on their property. They narrowed their choices down to companies. Molly maids company charges a flat rate of $100 per hour. Sparkly clean company charges $80 per hour plus $260 equipment fee. A) determine and state the number of hours that must be worked for the cost of both companies to be the same. B) if it is estimated to take at least 30 hours to company the job, which company will be less expensive? Justify your answer.

A. 13 hours

B. Sparkly clean company

Step-by-step explanation:

Step one:

given

Molly maids company

charges a flat rate of $100 per hour

let the total charges be y

let the number of hours be x

the expression for the total charges for Molly maids is

y=100x1

Step two:

Sparkly clean company

charges $80 per hour

equipment fee=$260

let the total charges be y

let the number of hours be x

the expression for the total charges for Sparkly clean  is

y=80x+2602

A) determine and state the number of hours that must be worked for the cost of both companies to be the same.

Equate equations 1 and 2

100x=80x+260

solve for x, collect like terms

100x-80x=260

20x=260

divide both sides by 20

x=260/20

x=13 hours

B) if it is estimated to take at least 30 hours to company the job, which company will be less expensive

x=30

Molly maids company

y=100x

y=100*30

y=3000

$3000

Sparkly clean company

y=80x+260

y=80*30+260

y=2400+260

$2660

Sparkly clean company  will be less expensive for a 30 hour work

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.