Bus Stops

(Source: Mathematics Teaching in the Middle School, Oct 1995)

Some people got on a bus. At the first stop, 2/ 5 of the people got off and 3/ 5 of the original number got on. At the second stop, _ of the people got off and 1/ 3 of the number that was left on the bus got on. At the last stop, _ of the people got off, leaving 5 people on the bus. How many people were on the bus before the bus reached the first stop?

Since so many students at UGA rely on the transit system (either through UGA or Athens-Clarke County), I will allow you to explore what both transit systems offer: (Please click on one of the icons below...the dawg - for the UGA transit and THE BUS for Athens-Clarke County transit...thanks to Best-Of-Web.com and http://www.gifs.net/for the great animated gifs...and to http://www.webplaces.com/html/sounds.htm for great sounds.)

I browsed through some of the routes The Bus takes on its daily mission and I found that I have been on route 14 many times as an undergraduate. To visit and check schedules click The Bus Athens Transit.

Now, let's reexamine the problem using some real-life pertinent information:

Bus departs from UGA ARCHES

UGA North & South Campus

UGA Family Housing
University Commons Apartments

Milledge Place Apartments

Carousal Village Apartments

Raintree Luxury Apartments

Some people got on The Bus....at the UGA Arches.

Since so many students have early morning classes, I would make the inference that

x = 15 people on the bus originally

At the first stop, (UGA North & South Campus), 2/ 5 of the people got off and 3/ 5 of the original number got on.

2/5 (15) = 6 people get off

so 15 - 6 = 9 people are left on the bus right now

3/5 (15) = 9 people get on

9 people left + 9 people that get on = 18 people now on bus

At the second stop, (UGA Family Housing), _ of the people got off and 1/ 3 of the number that was left on the bus got on.

since 18 people are now on the bus at the 2nd stop, the only fraction that made any sense was

1/6 of the number that was left after the first stop, so

1/6 (18) = 3 people got off

now, 18 - 3 = 15 people are left on the bus

1/3 (15) = 5 people got on

15 + 5 = 20 are now on the bus after the second stop

At the last stop, (University Commons Apartments), _ of the people got off, leaving 5 people on the bus.

since so many students live at the University Commons Apartments, many students will get off at this stop for rest, lunch, etc...so....

3/4 (20) = 15 people got off

now, 20 - 15 = 5 people are left on The Bus to continue on

!!!!!

How many people were on the bus before the bus reached the first stop?

15

Return