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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.