Question 1207775: Therese, an outside salesperson, uses her car for both business and pleasure. Last year, she traveled 30,000 miles, using 900 gallons of gasoline. Her car gets 40 miles per gallon on the highway and 25 in the city. She can deduct all highway travel,but no city travel, on her taxes. How many miles should Therese be allowed as a business expense?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!
Question only asks about distance traveled on highway; the highway travel distance
is what can be "deducted" for tax.
R, fuel efficiency
V, volume of fuel, gallons
D, distance
RV=D basic rule
If distance on highway was x,
ROAD FUEL EFF. VOL.fuel DISTANCE
HIGWAY 40 x/40 x
CITY 25 (30000-x)/25 30000-x
Total 900 30000
See the useful equation is sum of the volumes.
 ----------simplify and solve for x.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Therese, an outside salesperson, uses her car for both business and pleasure.
Last year, she traveled 30,000 miles, using 900 gallons of gasoline.
Her car gets 40 miles per gallon on the highway and 25 in the city.
She can deduct all highway travel, but no city travel, on her taxes.
How many miles should Therese be allowed as a business expense?
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Let "h" be the gallons oh highway; let "c" be the gallons in the city.
Then, from the problem description, you have these two equations for your unknowns
h + c = 900 (1) (total gallons spent last year)
40*h + 25*c = 30000 (2) (total distance, in miles, traveled last year)
Your intermediate goal is to find h, the gallons on highway.
From equation (1), express c = 900-h and substitute it for c in equation (2).
You will get then
40h + 25(900-h) = 30000.
Thus you have single equation for your unknown h.
Simplify and find h
40h + 25*900 - 25h = 30000,
40h + 25*900 - 25c = 30000,
40h - 25h = 30000 - 25*900
15h = 7500
h = 7500/15 = 500.
Thus we found that last year Theresa was allowed 500 gallons on highway.
Hence, the allowed distance on highway was 40*500 miles, or 20,000 miles.
At this point, the problem is solved in full.
ANSWER. Theresa was allowed 20,000 miles on highway for business expenses last year.
Solved.
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Post-solution note.
In my solution, I used two equations in two unknowns.
But the problem can be solved similarly, using one unknown h, too.
Using only one unknown for the highway gallons h, the setup equation is
40h + 25(900-h) = 30000 miles.
You can solve it then by the same way as I solved it in my solution above.
I presented the solution with two unknown only to make your understanding easier.
Simply so that you don't have to jump over the abyss in two leaps.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
This is basically a "mixture" problem -- you are mixing miles driven at 40 mpg on the highway and miles driven at 25 mpg in the city.
Here is a solution by a method that does not use algebra. This method can be used to solve any 2-part mixture problem.
All 900 gallons used on the highway at 40 mpg would make a distance of 36,000 miles; all 900 gallons in the city at 25 mpg would make a distance of 22,500 miles.
Look at the three mileages 22,500, 30,000, and 36,000 (on a number line, if it helps) and observe/calculate that 30,000 is 7500/13500 = 5/9 of the distance from 22,500 to 36,000.
That means 5/9 of the gallons were used at the higher rate.
5/9 of 900 gallons is 500 gallons, so she used 500 gallons for her highway driving.
500 gallons at 40 mpg is 20,000 miles.
ANSWER: 20,000 miles
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