Algebra 2 math help

Question

You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given:

g(x) = 3.45(18000/ old miles per gallon) -3.45(18000/ new miles per gallon)

g(x) calculates the dollar savings for one year for driving a car that gets higher miles per gallon rate.

a. In the formula what do you find when you divide 18000/old miles per gallon 

b. The car you drive now gets 18 mpg; the car you are looking to buy will get 27 mpg. How many dollars will you save in the first year by switching to the 27 mpg car?

c. How much would you save after 5 years?

d. The other car you are considering buying will get 33 mpg, but it costs $3000 more than the 27 mpg car. Would the additional savings in gas be worth the extra $3000 over a 5 year loan?

e. What gas mileage would your new car have to be if you saved $800 per year over your 18 mpg current car?

Answer 1

Pretty basic stuff.

a) Do a units analysis: (miles) / (old miles/gallon) = gallons. It's the number of gallons your old care consumes in driving 18,000 miles

b) Plug 18 mpg and 27 mpg into g(x):

g(x) = $3.45(18,000/18) - $3.45(18.000/27) = $_____

c) Multiply your answer from (b) by 5

d) Plug 18 mpg and 33 mpg into g(x) like we did in step (b), then multiply by 5. Subtract this answer from your answer to (c). If the difference is equal to or greater than $3000 then it's worth it.

e) Set g(x) = $800 and old miles per gallon = 18 mpg then solve for new miles per gallon:

$800 = $3.45(18,000/18) - $3.45(18,000/new miles per gallon)