Question

sebastion is deciding between two lawn mowing companies. Lovely Lawns charges a one-time fee of $20 plus $55 per week. Green Grass charges a one-time fee of $80 plus $40 per week. At how mant weeks of work will the total cost be the same for both the lawn mowing companies?

Answer 1

To determine when the costs from both Lovely Lawns and Green Grass are the same, we set up an equation: $20 + $55 per week equals $80 + $40 per week. After solving, we find that the total cost for both companies is the same after 4 weeks of work.

Step-by-step explanation:

Sebastian is evaluating two lawn mowing companies to determine when the total costs from each company would equal each other. This type of problem can be solved by setting up an equation where the total cost of service from Lovely Lawns is equal to the total cost of service from Green Grass. We will define two equations, one for each company, and solve for the number of weeks of work (w) where the costs are equal.

Lovely Lawns costs: One-time fee of $20 + $55 per week.
Green Grass costs: One-time fee of $80 + $40 per week.

To find when the costs are the same, we set up the equation:
20 + 55w = 80 + 40w.
We then solve for w by subtracting 40w from both sides:
20 + 15w = 80.
Subtract 20 from both sides:
15w = 60.
Divide both sides by 15 to solve for w:
w = 4.

Therefore, after 4 weeks of work, the total cost for both lawn mowing companies is the same.

Answer 2

After setting up the equations for both lawn mowing services and equating them, we find that the total cost for Lovely Lawns and Green Grass will be the same after 4 weeks.

Step-by-step explanation:

Sebastian is trying to determine when the total cost of two different lawn mowing services, Lovely Lawns and Green Grass, will be the same. To find this, we must set up an equation based on the information provided:

Lovely Lawns: $20 + $55 per week
Green Grass: $80 + $40 per week

If we let w be the number of weeks, we can express the total costs for each company as follows:

• Lovely Lawns: Total Cost = 20 + 55w
• Green Grass: Total Cost = 80 + 40w

To find out when the costs will be the same, we set the total costs equal to each other:

20 + 55w = 80 + 40w

To solve for w, subtract 40w from both sides:

20 + 15w = 80

Then, subtract 20 from both sides:

15w = 60

Finally, divide both sides by 15 to find the number of weeks:

w = 4

Therefore, after 4 weeks, the total cost for both lawn mowing companies will be the same.