Question 82895
I come up with $22.50 starting out.
Say he has x cents to start with
{{{x-50}}}cents after the 1st entrance toll
{{{(x-50)/2}}} after the 1st store
{{{(x-50)/2 - 50}}} after paying the 1st exit toll. That equals
{{{(x-150)/2}}}
{{{(x-150)/2 - 50}}} after the 2nd entrance toll. That equals
{{{(x-250)/2}}}
{{{(x-250)/4}}} after the 2nd store
{{{(x-250)/4 - 50}}} after the 2nd exit toll. That equals
{{{(x-450)/4}}}
{{{(x-450)/4 - 50}}} after the 3rd entramce toll. That equals
{{{(x-650)/4}}}
{{{(x-650)/8}}} after the 3rd store
{{{(x-650)/8 - 50}}} after the 3rd exit toll. That equals
{{{(x-1050)/8}}}
{{{(x-1050)/8 - 50}}} after the 4th entrance toll. That equals
{{{(x-1450)/8}}}
{{{(x-1450)/16}}} after the 4th store
{{{(x-1450)/16 - 50}}} after the 4th exit toll. That equals
{{{(x-2250)/16}}}
At that point he has nothing left
{{{(x-2250)/16 = 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