Prince Atif continued on his quest for hisPrincess Laiba after finding out the b

Question

Prince Atif continued on his quest for hisPrincess Laiba after finding out the building in which she had beenkept captive by evil-warlord Jaffer ). Whiletravelling, he stumbled upon a humble village called Al Hazara inthe kingdom of Parzania. The village had a very rustic and simpleambience in comparison with the other places he had seen inParzania. He decided to have some grub and take refuge in thevillage for the night. However, he realised he had run out ofmoney. He sat down sadly patting his camel, pondering what to donext. Three mischievous-looking children, who introduced themselvesas Rehan, Fatma and Aysha, understood his plight and decided tohelp him out. They took him to a shop and told him that the ownerof the shop was a cruel man who had duped several people of theirmoney. They suggested he steal some food from the shop to satiatehis hunger, and, in the process, avenge those cheated byshopkeeper. Prince Atif agreed and with their help stole a hugepile of expensive-looking dates. He divided the dates into twoequal portions: one for himself and his camel and the other for thethree children and asked them to divide it equally amongstthemselves. After that he thanked them and retired for thenight.

Before retiring, the kids decided to count the dates. They foundthat the dates were less than a hundred in number. During thenight, Rehan woke up, slyly counted the dates, and found that hecould segregate the dates into 3 equal portions, if he took one forhimself. He took a date and ate it up. Then, he took a third of therest for himself, hid them and went off to sleep. Shortly afterthat, Fatma awoke, counted the dates and found that she couldseparate the dates into 3 equal portions if she took one forherself. Like Rehan, she also took a date, gobbled it up and hid athird of the rest for herself and went to sleep. Later that night,Aysha also woke up, did the same thing and slept off. After wakingup in the morning, when they counted the dates, they found that theremaining dates could be divided into 3 portions if a date wasremoved from the pile. How many dates, in all, had been stolen byPrince Atif and the kids? Provide a detailed solution along withyour answer.

Explanation / Answer

We know that the final answer can be split into three equalparts if one is removed so that number is:
3x + 1, where x is an integer
Now moving backwards Aysha had taken a third. So if there werez she took 1/3 * z leaving 3x + 1. Mathematically,
z - 1/3 * z = 3x + 1 2/3z = 3x + 1 z = 3(3x + 1) / 2
Before she took a third she had eaten one so we add back inone. This is the number that Fatma left.
3(3x + 1) / 2 + 1
Repeating this process for Fatma:
3( 3(3x + 1) / 2 + 1 ) / 2 + 1
Repeating this process for Rehan:
3( 3( 3(3x + 1) / 2 + 1 ) / 2 + 1 )/ 2 + 1 = 81/8 x + 65/8
This is the number of dates the three started with. We knowthis is less than 100. We know that x is an integer. We know thatthis number must be an integer. So plug in for x until this numberis the largest integer less than 100.
And don't forget to multiply by 2 to account for the prince'sshare!
Hope this helps! Keep helping others!

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