Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor. Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.
If it takes 25 hours to paint Paul’s house, the most cost effective company will be
Answer Choices:
Painting USA.
Upscale Home Painting.
Part B:
The cost of painting the house will be the same for both companies if the number of hours required to paint Paul’s house is
3 hours.
5 hours.
8 hours.
To determine the most cost-effective company, we need to calculate the total cost for each option.
For Painting USA:
Evaluation cost: $75.00
Labor cost: $25.00 per hour x 25 hours = $625.00
Total cost: $75.00 + $625.00 = $700.00
For Upscale Home Painting:
Evaluation cost: $0.00
Labor cost: $40.00 per hour x 25 hours = $1000.00
Total cost: $0.00 + $1000.00 = $1000.00
Therefore, the most cost-effective company is Painting USA with a total cost of $700.00.
Part B:
To find the number of hours where both companies have the same cost, we need to set up an equation.
Let x be the number of hours.
For Painting USA:
Total cost = Evaluation cost + (Labor cost per hour x number of hours)
$700.00 = $75.00 + ($25.00 x x)
For Upscale Home Painting:
Total cost = Evaluation cost + (Labor cost per hour x number of hours)
$1000.00 = $0.00 + ($40.00 x x)
Setting these two equations equal to each other:
$700.00 = $1000.00
$25.00x = $40.00x
Solving for x:
$15.00x = $300.00
x = $300.00 / $15.00
x = 20 hours
Therefore, the number of hours required to paint Paul's house for the cost to be the same for both companies is 20 hours.
are you sure about part B?
You're right, I apologize for the incorrect calculation. Let's reevaluate Part B.
For Painting USA:
Total cost = Evaluation cost + (Labor cost per hour x number of hours)
$700.00 = $75.00 + ($25.00 x x)
For Upscale Home Painting:
Total cost = Evaluation cost + (Labor cost per hour x number of hours)
$1000.00 = $0.00 + ($40.00 x x)
Setting these two equations equal to each other:
$700.00 = $1000.00
$25.00x = $40.00x
Solving for x:
$300.00 = $40.00x - $25.00x
$300.00 = $15.00x
x = $300.00 / $15.00
x = 20
Therefore, the number of hours required to paint Paul's house for the cost to be the same for both companies is 20 hours.