Question

The bus fare in a city is People who use the bus have the option of purchasing a monthly coupon book for With the coupon​ book, the fare is reduced to​ $0.50. How many times must someone use the bus so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon​ book? Express the total monthly cost to use the bus with a coupon​ book, f, as a function of the number of times in the month the bus is​ used, x. Then express the total monthly cost to use the bus without a coupon​ book, g, as a function of the number of times in the month the bus is​ used, x.

Answer 1

26 times

Explanation:

The question has missing details. However, the given parameters are

Given

Without Coupon

Bus Fare = $2.00

With Coupon

Coupon = $39.00

Bus Fare = $0.50

Represent the number of fares with x

Without Coupon, cost of fares is

Cost = 2x

i.e.

f(x) = 2x

With Coupon, cost of fares is

Cost = 39 + 0.5x

i.e.

g(x) = 39 + 0.5x

To calculate when both fares will be equal, we must have:

f(x) = g(x)

2x = 39 + 0.5x

Collect like terms

2x - 0.5x = 39

1.5x = 39

Solve for x

x = 39/1.5

x = 26

This implies that, for both cost to be equal, the person must go 26 times