Hi Alexander.
There is a way to solve this using introductory algebra.
If you spend $5 on the first trip, then the second trip costs $5 + $10 (which is $15).
If you spend $11 on the first trip, then the second trip costs $11 + $10 (which is $21).
So we can say in general that if you spend x dollars on the first
trip, then the second trip costs x + 10 dollars.
The third trip costs $10 more than the second trip, and so on. Here
are all the trips:
1st trip: 
x 
2nd trip: 
x + 10 
3rd trip: 
x + 10 + 10 (which makes x + 20) 
4th trip: 
x + 20 + 10 (which makes x + 30) 
5th trip: 
x + 40 
... 

10th trip: 
x + 90 
Now we know how much each trip costs, so if we add them up, we get the
total amount. Let's do that:
x + (x + 10) + (x + 20) + (x + 30) + (x+40) + (x + 50) +
(x + 60) + (x + 70) + (x + 80) + (x + 90)
= 10x + 450
But the question says that we had $600 to spend in all. Assuming we
spend it all, then the total we got above (10x + 450) must be $600.
So we write:
10x + 450 = 600
Can you "solve for x" (in other words, find out what value x must have
to make that equation work)?
Hope this helps,
Stephen La Rocque.
