Section 6.3 Homework

Question

The bus fare is $2.00. People who use the bus can buy a monthly coupon book for $28. The fate is reduced to $1. Determine the number of times in a month

Answer 1

The bus fare is currently $2.00 per ride. However, commuters have the option of purchasing a monthly coupon book for $28, which reduces the fare to $1.00 per ride.

To determine how many times a commuter would need to ride the bus in a month to make the coupon book a cost-effective option, we can set up the following equation:

2x = 28 + y

Where x is the number of rides taken in a month at the regular fare of $2.00, y is the number of rides taken in a month using the coupon book fare of $1.00, and 2x represents the total cost of riding the bus without the coupon book.

To solve for y, we can simplify the equation:

y = 2x - 28

Then, we can plug in different values for x to find the corresponding value of y. For example, if a commuter rides the bus 14 times in a month without the coupon book, they would spend a total of $28. However, if they purchase the coupon book for $28 and use it for the remainder of their rides, they would spend only $14 on fares for a total savings of $14. Therefore, the break-even point for purchasing the coupon book would be 15 or more rides in a month.