Therese, an outside salesperson, uses her car for both business and pleasure. Last year, she travelled 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?

Let x = number of miles Therese should be allowed as a business expense.

I know she travelled a total of 30,000 miles last year using 900 gallons of gasoline to complete all those miles.

My confusion happens after reading about the 40 miles per gallon on the highway and the 25 miles per gallon in the city.

What is the equation set up?

Let "x" be the number of miles she traveled on the highway. Then she traveled 30000- x miles in the city. Since she gets 40 miles/gallon on the highway she used x miles/(40 miles/gallon)= x/40 gallons in the country. Since she gets 25 miles/gallon in the city she used (30000- x miles)/(25 miles/gallon)= (30000- x)/25 gallons. She used x/40+ (30000- x)/25= 900 gallons of gasoline.

Thank you for the equation and explanation.

x/40+ (30,000- x)/25= 900

5x + 240,000 - 8x = 180,000

-3x = 180,000 - 240,000

-3x = -60,000

x = -60,000/-3

x = 20,000

Therese should be allowed 20,000 miles as a business expense.