At my fruit stand, I sold half my watermelons and half a watermelon more in the first hour. In the second hour, I sold half my remaining watermelons and half a watermelon more. Incredibly enough in the third hour, I AGAIN sold half my remaining watermelons and half a watermelon more. In the fourth hour, I sold my last 6 watermelons. How many did I start with?

Guest Nov 21, 2019

#1**+1 **

Let the total watermelons we start with = N

1st hour sold = [ N/2 + 1/2]

Remaining is what we started with - number sold in 1st hour = N - [ N/2 + 1/2 ] = (1/2)N -1/2

2nd hour sold = (1/2)[ (1/2)N - 1/2] + 1/2 = [ (1/4)N + 1/4 ]

Remaining is what we started with at the end of the first hour - what we sold in the second hour =

[ (1/2)N - 1/2 ] - [ (1/4)N + 1/4] = [ (1/4)N - 3/4 ]

In the third hour we sold

(1/2) [ (1/4)N - 3/4 ]+ 1/2 = [ (1/8)N + 1/8]

What we have remaining is the what we started with at the end of the second hour - what we sold in the third hour =[(1/4)N - 3/4] - [ (1/8)N + (1/8) ] = (1/8)N - 7/8

And the number remaining = 6 ...so...

(1/8)N - 7/8 = 6 multiplty through by 8

N - 7 = 48

N = 55 is what we started with

CPhill Nov 21, 2019