SOLUTION: On the first day, I cycled 1/2 of the distance. On day 2, I cycled one half of the remaining distance. On day 3, I cycled three quarters of the remaining distance. On day 4, I cycl

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Question 932114: On the first day, I cycled 1/2 of the distance. On day 2, I cycled one half of the remaining distance. On day 3, I cycled three quarters of the remaining distance. On day 4, I cycled 10 miles.
On day 5 I cycled 2/3 of the remaining distance and on the final day I cycled the remaining 5 miles.
How far is it to my Grandmothers house?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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On the first day, I cycled 1/2 of the distance.
On day 2, I cycled one half of the remaining distance.
On day 3, I cycled three quarters of the remaining distance.
On day 4, I cycled 10 miles.
On day 5 I cycled 2/3 of the remaining distance and
on the final day I cycled the remaining 5 miles.
How far is it to my Grandmothers house?
:
Let d = distance to Grandma's house
End of day 1: 1%2F2d remains
End of day 2: 1%2F2 * 1%2F2d = 1%2F4d remains
End of day 3: 1%2F4d * 1%2F4 = 1%2F16d remains
End of day 4: 1%2F16d - 10 mi remain
End of day 5: 1%2F3(1%2F16d - 10) = 5 (remained for the last day)
1%2F48d - 10%2F3 = 5
1%2F48d = 5 + 10%2F3
1%2F48d = 15%2F3 + 10%2F3
1%2F48d = 25%2F3
multiply both sides by 48
d = 16(25)
d = 400 miles to grandma's house