# Bus tour

Several people decide to make a trip, for which they rent a vehicle for 522 euros and agree to pay each one according to the expense incurred. During the trip three of them decide to get off so that those who finished the trip had to pay 29 euros more than those who got off.

How many people started the trip?

#### Solution

7 people started the trip.
Approach:
We will call x to the total number of people who start the trip and Y at the price paid by those who decide to get off before arriving at the destination. According to the statement, we have to:

x * y + (x-3) * 29 = 522

And simplifying we get:
y = (609 - 29x) / x
y = (29 * (21 - x)) / x

This means that x (the number of people who start the trip) has to be a divisor of (21-x) since 29 is a prime number and x It has to be an integer value. Then it will be a divisor of 21:
x = 1 cannot be since 3 people could not get off.
x = 3 Nor is it a valid answer since no person would end the trip.
x = 7 It is the only valid solution.
x = 21 It would mean that the three who do not finish the trip would not pay anything.