Question

a local business was looking to hire a landscaper to work on their property. They narrowed their choices to two companies. Flourish Landscaping Company charges a flat rate of $120 per hour. Green Thumb Landscapers charges $70 per hour plus a $1600 equipment fee. Write a system of equations representing how much each company charges. Determine and state the number of hours that must be worked for the cost of each company to be same. [The use of the grid below is optional] If it is estimated to take at least 35 hours to complete the job, which company will be less expensive? Justify your answer

Answer 1

Flourish- 120x

Green Thumb- (70x)=1600

Flourish- 120*35= $4200

Green Thumb- (70*35)+1600= $4050

It would be less expensive to hire Green Thumb Landscapers. There is a $150 difference between the two. It would take 32 hours of work for the cost to be the same for both companies

Hope this helps!

Answer 2

The system of equations representing how much each company charges.

Flourish Landscaping Company:
`y=120x`

Green Thumb Landscapers:
`y=70x+1600`

The number of hours they must be worked for the cost of each company to be same is 32 hours.

For 35 hours of job Green Thumb Landscapers will be less expensive.

Explanation:

Consider the provided information.

Part (A)

Let x be the number of hours and y is the total cost.

It is given that the Flourish Landscaping Company charges a flat rate of $120 per hour.

This can be written as:

`y=120x`

Green Thumb Landscapers charges $70 per hour plus a $1600 equipment fee.

This can be written as:

`y=70x+1600`

Thus, the system of equations representing how much each company charges is:

Flourish Landscaping Company:
`y=120x`

Green Thumb Landscapers:
`y=70x+1600`

Part (B)

Now we need to determine the hours that must be worked for the cost of each company to be same.

It is given that the cost of both company must be same that means the value of y is equal, this can be written as:

`120x=70x+1600`

Now solve for x.

`120x-70x=1600`

`50x=1600`

`x=32`

The number of hours they must be worked for the cost of each company to be same is 32 hours.

Part(C)

Now we need to find for 35 hours of job which company will be less expensive.

So substitute the value of x = 35 in both the equation as shown:

For Flourish Landscaping Company:

`y=120(35)`

`y=4200`

Flourish Landscaping Company charge $4200 for 35 hours of job.

Now substitute the value of x = 35 in
`y=70x+1600`

For Green Thumb Landscapers:

`y=70(35)+1600`

`y=2450+1600`

`y=4050`

Green Thumb Landscapers charge $4050 for 35 hours of job.

Hence, for 35 hours of job Green Thumb Landscapers will be less expensive.