How many miles should Jane be allowed as a business expense?

Question
Jane Manning, an outside business woman, uses her car for both business and pleasure. Last year, she traveled 30,000 miles using 900 gallons of gas. Her car gets 40 miles per gallon on the Highway, and 25 mpg in the city. She can deduct all highway travel, but no city travel, on her taxes.

How many miles should Jane be allowed as a business expense?



Solution

Let x = gas spent in the Highway

y = gas spent in the City

Therefore,
Equation 1: x + y = 900

Therefore,

Equation 2: 40x + 25y = 36,000

Transform

Equation 1 to x = 900 – y

Substitute the above equation in Equation 2

Which is equal to 36,000 – 40y + 25y = 30,000

Simplify the above equation to 6,000 = 15y

Hence, y = 400 AND x = 500

Therefore, Jane can deduct 500 gallons OR 10,000 miles on her taxes.

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