SOLUTION: Alvin has many apples. He gives 1/3 of his apples plus 2/3 of an apple to Bob. He then gives 1/4 of his remaining apples plus half an apple to Chris. Afterwards, he gives half

Question 1137873: Alvin has many apples. He gives 1/3 of his apples plus 2/3 of an apple to Bob.
He then gives 1/4 of his remaining apples plus half an apple to Chris.
Afterwards, he gives half of his remaining apples to David.
Lastly, he gives half of his remaining apples plus half an apple to Ed.
In the end, Alvin has 5 apples left. How many apples does Alvin have initially?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Work backwards.

In the end, Alvin has 5 apples left.

Lastly, he gives half of his remaining apples plus half an apple to Ed.

Before this, Alvin had 11 apples.

Afterwards, he gives half of his remaining apples to David.

Before this, Alvin had 22 apples.

He then gives 1/4 of his remaining apples plus half an apple to Chris.

Before this, Alvin had 30 apples.

He gives 1/3 of his apples plus 2/3 of an apple to Bob.

Before this, Alvin had 46 apples.

Alvin started out with 46 apples.

Double-check:

He starts with 46 apples and gives 1/3 of his apples (15.33 apples) + 2/3 of an apple (0.67 apples) to Bob. That's 16 apples. Giving away 16 apples from 46 leaves him with 30 apples.

He has 30 apples and gives 1/4 of his apples (7.5 apples) + 1/2 of an apple (0.50 apples) to Chris. That's 8 apples. Giving away 8 apples from 30 leaves him with 22 apples.

He has 22 apples and half his apples (11 apples) to David. Giving away 11 apples from 22 leaves him with 11 apples.

He has 11 apples and give half his apples (5.5 apples) + 1/2 of an apple (0.5 apples) to Ed. That's 6 apples. Giving away 6 apples from 11 leaves him with 5 apples.
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