## Monday, July 27, 2009

### Chewing Gum Treat

A kid comes to the store with his piggy bank. He does not have enough money to buy a colorful chewing gum that he really wants, so his mom lends him exactly the same amount as he already has. Kid pays \$1 for the chewing gum, takes the change and leaves. On a second week, kid comes to the store with his dad. Again, he convinces his dad that he really deserves this colorful chewing gum, dad lends him exactly the same amount as kid has, kid buys the gum, takes change and leaves. On a third week, grandmother sponsors the kid in a similar manner. And on a fourth week, kid does this trick on his older sister. After borrowing from her and buying the gum, he has no more money left.
How much did he have in the piggy bank to start with?

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Alin Grin said...
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Alin Grin said...
This comment has been removed by the author.
Alin Grin said...
This comment has been removed by the author.
Alin Grin said...

2d-1=0 Therefore: d=0.5
2c-1=d Therefore: c=0.75
2b-1=c Therefore: b=0.875
2a-1=b Therefore: a=0.9375

Maria said...

That's right!

You started from the last gum purchased and untangled it step-by-step to the first purchase.
d is the amount that kid had on his 4th store visit with his sister (before borrowing another d from her);
c is the amount kid had when entering the store with his grandma, before she gave him another c;