Jack decided to get help with his back yard. He looked up local contractors and got costs from four contractors. These contractors had different hourly rates and different base fees.

Question

In each equation,
is the cost per hour for the contractor. Find the contractor that has the lowest hourly rate.

Responses
A Econo-Heights,
Econo-Heights, 469 point 5 0 dollars is equal to 3 x plus 175 dollars
B Landscaping to the Heights,
Landscaping to the Heights, 469 point 5 0 dollars is equal to 6 x plus 75 dollars
C Mile High Landscaping,
Mile High Landscaping, 469 point 5 0 dollars is equal to 4 x plus 150 dollars
D Mountain Air Yard Service,

Answer 1

To find the contractor with the lowest hourly rate, we need to analyze each equation given for the total cost, which is structured as:

\[ \text{Total Cost} = \text{Hourly Rate} \times \text{Hours Worked} + \text{Base Fee} \]

In this case, the structure of the equations for the four contractors is as follows:

A. Econo-Heights: \( 469.50 = 3x + 175 \)

B. Landscaping to the Heights: \( 469.50 = 6x + 75 \)

C. Mile High Landscaping: \( 469.50 = 4x + 150 \)

D. Mountain Air Yard Service: (not provided; we'll need to use only A, B, and C for comparison).

Let's solve for \( x \) (the hourly rate) in each case:

A. Econo-Heights

1. Start with:
   \( 469.50 = 3x + 175 \)
2. Subtract 175 from both sides:
   \( 469.50 - 175 = 3x \)
   \( 294.50 = 3x \)
3. Divide by 3:
   \( x = \frac{294.50}{3} \)
   \( x = 98.17 \) (approximately)

B. Landscaping to the Heights

1. Start with:
   \( 469.50 = 6x + 75 \)
2. Subtract 75 from both sides:
   \( 469.50 - 75 = 6x \)
   \( 394.50 = 6x \)
3. Divide by 6:
   \( x = \frac{394.50}{6} \)
   \( x = 65.75 \) (approximately)

C. Mile High Landscaping

1. Start with:
   \( 469.50 = 4x + 150 \)
2. Subtract 150 from both sides:
   \( 469.50 - 150 = 4x \)
   \( 319.50 = 4x \)
3. Divide by 4:
   \( x = \frac{319.50}{4} \)
   \( x = 79.875 \) (approximately)

Summary of Hourly Rates

• Econo-Heights: \( x \approx 98.17 \)
• Landscaping to the Heights: \( x \approx 65.75 \)
• Mile High Landscaping: \( x \approx 79.875 \)

Conclusion

Landscaping to the Heights has the lowest hourly rate at approximately \( 65.75 \) dollars per hour.

Answer 2

The answer is??

Answer 3

The contractor with the lowest hourly rate is Landscaping to the Heights, with an approximate hourly rate of $65.75.