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A certain car model cost Birr 20,000 with a gasoline engine and Br 25,000 with a diesel engine. The number of miles per gallon of fuel for cars with these two engines is 25 and 30, respectively. Assume that the price of both types of fuel is Birr 1.50 per gallon.
Required:
a) Drive the equation for the cost of driving a gasoline powered car.
b) Drive the equation for the cost of driving a diesel powered car.
c) Find the break-even point, that is, find the mileage at which the diesel-powered car becomes more economical than the gasoline powered car.
asked by Mesay girum
June 29, 2021
5 answers
"derive" not "drive"
cost in $/mi is just mi/(mi/gal) * $/gal
so, the cost of driving x miles is
(a) 20000 + x/25 * 1.50 = 0.06x + 20000
do the same for (b) and then solve for (c)
answered by oobleck
June 29, 2021
number of miles driven = x
cost to drive the gas car = 20000 + x/20 * 1.5 = 3x/40 + 20000
cost to drive the diesel - 25000 + x/30*1.5 = x/20 + 25000
3x/40 + 20000 = x/20 + 25000
3x/40 - x/20 = 5000
x/40 = 5000
x = 20,000
answered by mathhelper
June 29, 2021
oops, copy error !!
I used 20 instead of 25 in line #2
Make the necessary changes, or else solve oobleck's equation
answered by mathhelper
June 29, 2021
good
answered by Esubalew Tesfaye
August 31, 2021
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1300 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
answered by Samantha
July 16, 2022
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Ask a New Question
A certain car model cost Birr 20,000 with a gasoline engine and Br 25,000 with a diesel engine. The number of miles per gallon of fuel for cars with these two engines is 25 and 30, respectively. Assume that the price of both types of fuel is Birr 1.50 per gallon.
Required:
a) Drive the equation for the cost of driving a gasoline powered car.
b) Drive the equation for the cost of driving a diesel powered car.
c) Find the break-even point, that is, find the mileage at which the diesel-powered car becomes more economical than the gasoline powered car.
asked by Mesay girum
June 29, 2021
5 answers
"derive" not "drive"
cost in $/mi is just mi/(mi/gal) * $/gal
so, the cost of driving x miles is
(a) 20000 + x/25 * 1.50 = 0.06x + 20000
do the same for (b) and then solve for (c)
answered by oobleck
June 29, 2021
number of miles driven = x
cost to drive the gas car = 20000 + x/20 * 1.5 = 3x/40 + 20000
cost to drive the diesel - 25000 + x/30*1.5 = x/20 + 25000
3x/40 + 20000 = x/20 + 25000
3x/40 - x/20 = 5000
x/40 = 5000
x = 20,000
answered by mathhelper
June 29, 2021
oops, copy error !!
I used 20 instead of 25 in line #2
Make the necessary changes, or else solve oobleck's equation
answered by mathhelper
June 29, 2021
good
answered by Esubalew Tesfaye
August 31, 2021
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1300 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
answered by Samantha
July 16, 2022
Answer this Question
Your Name
Hundera
Your Answer
Still need help?
You can ask a new question or browse more mathematics questions.
Similar Questions
A certain car model cost Birr 20,000 with a gasoline engine and Br 25,000 with a diesel engine. The number of miles per gallon of fuel for cars with these two engines is 25 and 30, respectively. Assume that the price of both types of fuel is Birr 1.50 per
In its first year, Abol buna Company had the following experience.
Sales = 25,000 units Selling price = Birr 100 Total variable cost = Birr 1,500,000 TFC = Birr 350,000 Required: Develop revenues, cost, and profit functions for the company in terms of
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2. In its first year, “ABOL BUNA” Company had the following experience.
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A firm Manufactures & Markets a product that sells for birr 20 per unit. Fixed Costs Associated With activity total birr 40,000 a month. While Variable Cost Per unit is birr 10. A maximum of 10,000 units can be produced & Sold
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with activity total Birr 40,000 a month, while variable cost per unit is Birr 10. A maximum of 10,000 units can be produced and sold
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a) Sure, here's the equation for the cost of driving a gasoline-powered car:
Cost of driving = 20000 + (miles driven / 25) * 1.50
b) And here's the equation for the cost of driving a diesel-powered car:
Cost of driving = 25000 + (miles driven / 30) * 1.50
c) To find the break-even point where the diesel-powered car becomes more economical than the gasoline-powered car, we can set the two equations equal to each other and solve for the mileage:
20000 + (miles driven / 25) * 1.50 = 25000 + (miles driven / 30) * 1.50
Simplifying the equation, we have:
(1.50/25 - 1.50/30) * miles driven = 25000 - 20000
(0.06 - 0.05) * miles driven = 5000
0.01 * miles driven = 5000
miles driven = 5000 / 0.01
miles driven = 500000
So, the break-even point is 500,000 miles, at which the diesel-powered car becomes more economical than the gasoline-powered car.
To answer the questions:
a) To derive the equation for the cost of driving a gasoline-powered car, we need to consider the cost of fuel and the number of miles driven. The cost of driving x miles can be calculated by multiplying the number of gallons of fuel consumed by the price per gallon and adding it to the initial cost of the car.
In this case, the number of miles per gallon for a gasoline-powered car is 25 and the price of fuel is Birr 1.50 per gallon. The equation for the cost of driving a gasoline-powered car is:
Cost = 20,000 + (x/25 * 1.50) = 0.06x + 20,000
b) To derive the equation for the cost of driving a diesel-powered car, we follow the same process as in part a. The number of miles per gallon for a diesel-powered car is 30. The equation for the cost of driving a diesel-powered car is:
Cost = 25,000 + (x/30 * 1.50) = 0.05x + 25,000
c) To find the break-even point, we need to determine the mileage at which the cost of driving the diesel-powered car becomes more economical than the cost of driving the gasoline-powered car.
To do this, we set the equations for the cost of driving each type of car equal to each other and solve for x:
0.06x + 20,000 = 0.05x + 25,000
Simplifying the equation:
0.01x = 5,000
x = 5,000/0.01
x = 500,000
Therefore, the break-even point is at 500,000 miles. This means that if you plan to drive more than 500,000 miles, the diesel-powered car would be more economical than the gasoline-powered car.
To calculate the cost of driving a gasoline-powered car (a), use the equation:
Cost = Initial Cost + (Miles / MPG) * Price per Gallon
Given:
Initial Cost = Birr 20,000
Miles per Gallon (MPG) = 25
Price per Gallon = Birr 1.50
The equation becomes:
Cost = 20,000 + (Miles / 25) * 1.50
To calculate the cost of driving a diesel-powered car (b), use the equation:
Cost = Initial Cost + (Miles / MPG) * Price per Gallon
Given:
Initial Cost = Birr 25,000
Miles per Gallon (MPG) = 30
Price per Gallon = Birr 1.50
The equation becomes:
Cost = 25,000 + (Miles / 30) * 1.50
To find the break-even point (c), we need to find the mileage at which the cost of driving the diesel-powered car becomes less than the cost of driving the gasoline-powered car.
Set the two equations equal to each other and solve for Miles:
20,000 + (Miles / 25) * 1.50 = 25,000 + (Miles / 30) * 1.50
Simplifying the equation:
(1.50 / 25) * Miles - (1.50 / 30) * Miles = 25,000 - 20,000
Multiplying both sides by 150 to eliminate fractions:
6 * Miles - 5 * Miles = 5,000
Miles = 5,000
Therefore, the break-even point is at 5,000 miles. At or above 5,000 miles, the diesel-powered car becomes more economical than the gasoline-powered car.