Question

A bus route shows a very regular pattern one morning: 8 passengers get on at the first stop. From then on, 3 passengers get off and 5 passengers get on at every stop, until the entire bus is full. If the bus holds 45 passengers in all, at which stop does the bus fill up?

Answer 1

In each stop if 3 passengers get off and 5 passengers get on that means effectively 2 passengers get added to the bus at every stop. The bus starts with 8 passengers and the bus capacity is 45. So how many stops to fill up the bus?

Answer 2

I know the answer is 20... but how

Answer 3

The bus starts with 8 passengers after the first stop. The bus capacity is 45. That means (45-8 = 37) more people need to be added. From the second stop onwards 2 passengers effectively get added to the bus: So the number of stop we need to fill the bus is 37/2 = 18.5 stops. So after the first stop we need 18.5 more stops. So the total number of stops is first stop + 18.5 more = 19.5 stops. With 19 stops the bus still won't be full. We need 19.5 stops. But since .5 stop does not exist we need to round it to the next higher number which is 20 stops.

Answer 4

Ohhhh I see I see makes sense thank you!

Answer 5

And 8+2x>=45 can be used to express the situation right

Answer 6

Yes.

Answer 7

8+2x>=45 (where x is the number of stops counting from the second stop)
subtract 8 from both sides
2x >= 37
divide both sides by 2
x >= 18.5 stops
Since the number of stops has to be an integer x >= 19
But remember to include the first stop.
x >= 20. So the stop where the bus gets full is the 20th stop.