SOLUTION: Please help me with this question I apoligize if its under the wrong heading: Ramon was going to visit his friend in a distant city. He had to travel on four different turnpikes

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Question 82895This question is from textbook Algebra 1
: Please help me with this question I apoligize if its under the wrong heading:
Ramon was going to visit his friend in a distant city. He had to travel on four different turnpikes to get there. He had to pay 50 cents to enter each turnpike and 50 cents to exit. On each turnpike, he stopped at one store for a snack and spent 1/2 of the money he had after he entered that turnpike. After paying 50 cents to leave the last turnpike, Ramon was out of money. How much did he start with before entering the first turnpike? This question is from textbook Algebra 1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I come up with $22.50 starting out.
Say he has x cents to start with
x-50cents after the 1st entrance toll
%28x-50%29%2F2 after the 1st store
%28x-50%29%2F2+-+50 after paying the 1st exit toll. That equals
%28x-150%29%2F2
%28x-150%29%2F2+-+50 after the 2nd entrance toll. That equals
%28x-250%29%2F2
%28x-250%29%2F4 after the 2nd store
%28x-250%29%2F4+-+50 after the 2nd exit toll. That equals
%28x-450%29%2F4
%28x-450%29%2F4+-+50 after the 3rd entramce toll. That equals
%28x-650%29%2F4
%28x-650%29%2F8 after the 3rd store
%28x-650%29%2F8+-+50 after the 3rd exit toll. That equals
%28x-1050%29%2F8
%28x-1050%29%2F8+-+50 after the 4th entrance toll. That equals
%28x-1450%29%2F8
%28x-1450%29%2F16 after the 4th store
%28x-1450%29%2F16+-+50 after the 4th exit toll. That equals
%28x-2250%29%2F16
At that point he has nothing left
%28x-2250%29%2F16+=+0
x-2250+=+0
x+=+2250
So he started with $22.50
check answer
2200 after 1st entrance toll
1100 after 1st store
1050 after 1st exit toll
1000 after 2nd entrance toll
500 after 2nd store
450 after 2nd exit toll
400 after 3rd entrance toll
200 after 3rd store
150 after 3rd exit toll
100 after 4th entrance toll
50 after 4th store
0 after 4th exit toll
OK