Question

The daily number of riders on a certain bus route is 360, each of whom pay a 50¢ fare. The bus company has determined that for every fare increase of 5¢, there will be 20 fewer riders. What fare should the company charge in order to collect $196 per day from this route.

Answer 1

The answer is 70¢

Let x = the number of 5¢ fare increases

Let y = money the company gets

Equation: y = (360 - 20x) (0.50 + 0.05x)

Solve for x when y = 196

196 = 180 + 18x - 10x - x^2

x^2 - 8x + 16 = 0

Factor to solve for x

(x - 4)^2 = 0

x = 4

Remember what x means

Total fare = 0.50 + 0.05x = 0.50 + 0.20 = 0.70

Total fare = 70¢