# WORD PROBLEM- HELP

The bus fare in a city is $2.00. People who use the bus have the option of purchasing a coupon book for$27.00. With the coupon book, the fare is reduced to $1.00. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book? #### mmm4444bot ##### Super Moderator Staff member I'll get you started by organizing for you a chart of what's going on. $$\displaystyle \begin{array}{|c|c|c|}\hline {\text{Trip Number}&\text{Regular Fares}&\text{Book + Discounted Fares}}\\ \hline {1&2.00&28.00}\\ \hline{2&4.00&29.00}\\ \hline {3&6.00&30.00}\\ \hline {4&8.00&31.00}\\ \hline {5&10.00&32.00}\\ \hline{6&12.00&33.00}\\ \hline {7&14.00&34.00}\\ \hline {\vdots&\vdots&\vdots}\\ \hline \end{array}$$ The two "fare" columns represent running totals of the money paid out under each plan after 1 trip, 2 trips, 3 trips, et cetera. Does this make sense, so far? After taking 1 bus trip, a person with no discount has paid$2, while a person who bought a coupon book has paid a total of $28 ($27 for the book, and $1 for the discounted ride). After taking 2 bus trips, a person with no discount has paid a total of$4, while a person entitled to discounts has paid a total of $29 ($27 for the book, and \$1 each for the two discounted rides).

The exercise asks "how many trips"?

So, pick a variable to represent this unknown amount.

Let n = the number of trips

Now we can write an expression, using the variable n, to represent the total dollar amount spent (after taking n trips) for a person with no coupon book.

We can also write an expression to represent the total dollar amount spent (after taking n trips) for a person with a coupon book.

It's easy to find the number of trips where both totals are equal: set the two expressions equal (to form an equation), and then solve the equation for n.

Both columns represent arithmetic sequences. (Maybe, that's what your class is studying; I don't know because you gave us zero information about what you're thinking so far.)

Are these hints enough information for you to be able to continue?

Let us know, if you need more help. Please show whatever work you can, or explain why you're stuck.

Cheers ~ Mark 