Chase is deciding between two landscaping companies for his place of business. Company A charges $35 per hour and a $150 equipment fee. Company B charges $25 per hour and a $300 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t, commat, and determine which company would be cheaper if Chase needs 16 hours of landscaping.

Question

Answer
Attempt 1 out of 2

A, equalsA=
B, equalsB=

is $
cheaper than
for 16 hours of landscaping.

Answer 1

To find the cost of landscaping from each company, we can set up the equations based on the information given:

For Company A:

• Hourly rate: $35
• Equipment fee: $150

The total cost \( A \) for \( t \) hours of landscaping with Company A can be expressed as: \[ A = 35t + 150 \]

For Company B:

• Hourly rate: $25
• Equipment fee: $300

The total cost \( B \) for \( t \) hours of landscaping with Company B can be expressed as: \[ B = 25t + 300 \]

Now, we need to calculate the costs for 16 hours of landscaping (\( t = 16 \)) for each company.

For Company A: \[ A = 35(16) + 150 \] \[ A = 560 + 150 \] \[ A = 710 \]

For Company B: \[ B = 25(16) + 300 \] \[ B = 400 + 300 \] \[ B = 700 \]

Now, we can determine which company is cheaper for 16 hours of landscaping.

• Cost of Company A: $710
• Cost of Company B: $700

Thus, the answer to your statement would be: Company B is $10 cheaper than Company A for 16 hours of landscaping.

To summarize: \[ A = 35t + 150 \] \[ B = 25t + 300 \] And for 16 hours of landscaping: Company B is $10 cheaper than Company A.