## How many miles required to be driven for both services cost, Mathematics

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Easy Rider taxi service charges a pick-up fee of \$2 and \$1.25 for each mile. Luxury Limo taxi service charges a pick-up fee of \$3.25 and \$1 per mile. How many miles required to be driven for both services to cost the same amount?

Let x = the number of miles traveled in the taxi. The expression for the cost of a ride with Easy Rider would be 1.25x + 2. The expression for the cost of a ride along with Luxury Limo is 1x + 3.25. To solve, set the two expressions equal to each other: 1.25x + 2 = 1x + 3.25. Subtract 2 from both sides: 1.25x + 2 - 2 = 1x + 3.25 - 2. This simpli?es to: 1.25x = 1x + 1.25; subtract 1x from both sides: 1.25x - 1x = 1x - 1x + 1.25. Divide both sides of the equation by .25: .25/.25 =1.25/.25. The variable is now alone:
x = 5; the cost would be the same if the trip were 5 miles long.

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