Help me figure this exercise out?

Question

A certain model car cost $14500 with a gasoline engine and 15450 with a diesel one.
The number of miles per gallon of fuel for these cars are respectively 22 and 31.
Assume that the price of each type of fuel is $1589 per gallon.
Find the cost Cg of driving the gasoline-powered car
Find the cost Cd of driving the diesel-powered car
Find the break-even point. That is find the mileage at which the diesel-powered car becomes more economical than the gasoline

Answer 1

Okay, lets see:
Put the whole thing into an equation.
The cost of fuel for gasoline car = 1589/22= 72.23
cost of fuel for diesel car =1589/31 = 51.26
So the cost per gallon for gasoline and diesel cars is $72.23 and $ 51.26 respectively
The equation for the gasoline car is:
y1 = 72.23x + 14500
equation for diesel car is:
y2 = 51.26x + 15450
Cost of driving gasoline car = 1589+14500 = $16089
Cost for driving the diesel car = 1589 + 15450 = $17039

The break even point is :
72.23x + 14500 = 51.26x + 15450
72.23x - 51.26x = 15450 - 14500
20.97x = 950
x = 45.3

So, the break even point is 45.3 dollars of fuel.

Hope that helped :)

Answer 2

the cost of drivinging the gas car is Cg= 1589(X/22)+14500
x=the # of miles

For the diesel car Cg=1589(X/31)+15450

For the break evenpoint 1589(X/31)+15450=1589(X/22)+14500

Solve for X then plug it back it.

1589(X/31)+15450=1589(X/22)+14500
1589(X/31)+950=1589(X/22)
(X/31)+950=(X/22)
950=(X/22)-(X/31)
20900=X+22X/31
647900=31X+22X
647900=53X
X=12224.53
Thus at aroun 12,225 miles the cost of drving the two cars is even

Answer 3

It's really easier than all that, and you will even get the right answer:

At 31 mpg and $1.589, fuel cost is $0.135/mi
At 22 mpg, it's $0.195

Difference is $0.067/mi.

Difference in price is $950.

Divide $950 by savings per mile ($0.067) to get 16667 miles - the break-even point.

Check

Cost $14500
Fuel for 16667 miles at $0.195/mi = $3250

Total = $17750

Cost $15450
Fuel for 16667 mikes at $0.168/mi = $2300

Total $17750

The Diesel saves $0.067/mi from here on out.