Cost analysis Te owner of a small construction busi-ness needs a new truck. He can buy a diesel truck for $38,000 and it will cost him $0.24 per mile to operate. He can buy a gas engine truck for $35,600 and it will cost him $0.30 per mile to operate. Find the number of miles he must drive before the costs are equal. If he normally keeps a truck for 5 years, which is the better buy?
costs are equal after x miles if
38000 + 0.24x = 35600 + 0.30x
Now you need to know how many miles/year he drives.
To find the number of miles the owner must drive before the costs are equal, we can set up the following equation:
38,000 + 0.24x = 35,600 + 0.30x
Where x represents the number of miles driven.
To solve this equation, we can start by simplifying:
0.06x = 2,400
Next, we can solve for x by dividing both sides of the equation by 0.06:
x = 2,400 ÷ 0.06
x = 40,000
Therefore, the owner must drive 40,000 miles before the costs of the two trucks are equal.
Now, let's compare the costs over a 5-year period. Since we know the cost per mile, we can calculate the total cost for each truck and then compare them.
For the diesel truck:
Total cost = 38,000 + (0.24 × 40,000) = 38,000 + 9,600 = 47,600
For the gas engine truck:
Total cost = 35,600 + (0.30 × 40,000) = 35,600 + 12,000 = 47,600
Both trucks have a total cost of $47,600 over 40,000 miles.
Therefore, in terms of cost, there is no significant difference between the two trucks. The choice between them would likely depend on other factors, such as personal preference or any specific requirements for the construction business.
To determine the number of miles the owner must drive before the costs are equal, we can set up an equation.
Let's assume the number of miles driven is represented by 'x'.
For the diesel truck:
The cost of purchasing the truck is $38,000.
The cost per mile to operate is $0.24.
We can calculate the cost of operating the diesel truck as:
Cost of operating diesel truck = (cost per mile) * (number of miles driven)
Cost of operating diesel truck = $0.24 * x
For the gas engine truck:
The cost of purchasing the truck is $35,600.
The cost per mile to operate is $0.30.
We can calculate the cost of operating the gas engine truck as:
Cost of operating gas engine truck = (cost per mile) * (number of miles driven)
Cost of operating gas engine truck = $0.30 * x
Now, we need to determine the point at which the costs are equal. We can set up an equation:
$38,000 + ($0.24 * x) = $35,600 + ($0.30 * x)
Simplifying the equation, we get:
$38,000 - $35,600 = ($0.30 * x) - ($0.24 * x)
$2,400 = ($0.06 * x)
Now, we can solve for 'x':
x = $2,400 / $0.06
x = 40,000
Therefore, the owner must drive 40,000 miles before the costs of the two trucks become equal.
To determine which truck is the better buy considering a 5-year period, we need to calculate the total cost of owning each truck over the 5-year period.
For the diesel truck:
Total cost of owning diesel truck = cost of purchasing the truck + (cost per mile * number of miles driven per year * number of years)
Total cost of owning diesel truck = $38,000 + ($0.24 * 40,000 * 5)
Total cost of owning diesel truck = $38,000 + $48,000
Total cost of owning diesel truck = $86,000
For the gas engine truck:
Total cost of owning gas engine truck = cost of purchasing the truck + (cost per mile * number of miles driven per year * number of years)
Total cost of owning gas engine truck = $35,600 + ($0.30 * 40,000 * 5)
Total cost of owning gas engine truck = $35,600 + $60,000
Total cost of owning gas engine truck = $95,600
Therefore, considering a 5-year period, the diesel truck is the better buy since the total cost of owning it over this period is less than the total cost of owning the gas engine truck.