Susie wants to rent a car for a day so that she can visit her sister at university. She has called two car rental companies. Rent-a-Heap charges $50 per day, plus $0.12/km. Kurt’s Rent-a-Car charges $40 per day, plus $0.20/km. At what distance will the cost of renting a car be the same from both companies?

125 km

Step-by-step explanation:

Write an equation where the car change and distance of both cars equal:

Cost of Car A + Cost per Km A x Distance = Cost of car B + cost per km B x Distance

50 + 0.12x = 40 + 0.20x

Solve the above equation:

50 + 0.12x = 40 + 0.20x

5000 + 12x = 4000 + 20x (Multiply both sides by 100)

12x = 20x - 1000 (Take 5000 from both sides)

-8x = -1000 (Subtract 20x from both sides)

x = (Simplify, remember a negative divide a negative is positive!)

x = 125

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