The bus fare in a city is 2.00. People who use the bus have the option of purchasing a monthly coupon book for 39.00. With the coupon book, the fare is reduced to 0.50.
That's nice.
To find out how many times a person needs to use the bus in a month for buying a coupon book to be cheaper than paying the regular fare, we can set up an equation.
Let's assume the number of times a person uses the bus in a month is x.
Without the coupon book:
Total cost = x * 2.00
With the coupon book:
Total cost = 39.00 (coupon book cost) + 0.50 (fare per ride)
To make the coupon book cheaper, we need to compare these two costs:
x * 2.00 > 39.00 + 0.50x
Let's solve this inequality to find the minimum value of x for the coupon book to be cheaper:
2.00x > 39.00 + 0.50x
2.00x - 0.50x > 39.00
1.50x > 39.00
x > 39.00 / 1.50
x > 26
So, if a person uses the bus more than 26 times in a month, it is more cost-effective for them to buy the coupon book.
To summarize:
- If a person uses the bus 26 or fewer times in a month, they should pay the regular fare of $2.00 per ride.
- If a person uses the bus more than 26 times in a month, they should buy the coupon book for $39.00. Each ride will then cost $0.50.