Question 56012: what is the difference, money-wise, between a half-dozen dozen dollar bills and six dozen donzen dimes?
Chip and Dale collected 32 acrons on monday and stored them with their acorn supply. After Chip fell asleep, Dale ate half the acorns. This pattern continued through friday night, with 32 acrons being added and half being eaten on saturday morning, chip counted the acrons and found that they had only 35. how many acorns had they started with on monday
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! A half-dozen dozen dollar bills would be 6 dozen dollar bills or $72.
Six dozen dozen dimes would be 6 * 144 dimes or 864 dimes. The value of this is of course $86.40.
The difference would be $14.40, or I guess you could say a dozen dozen dimes.
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On the Chip and Dale problem, the problem is not entirely clear to me, but I'll give it my best interpretation.
Let x = the original number of acorns. According to the problem, they added 32 acorns to their supply, giving them a total of x+32 acorns.
Next, Dale ate half of the acorns after Chip fell asleep. I will assume that it was still Monday when Dale first ate half of the acorns. This means that he ate half  and that left  of the acorns.
On Tuesday he ate half of what was left, leaving half:  .
On Wednesday, he ate half and left half, leaving  .
On Thursday, he ate half and left half, leaving  .
On Friday, he ate half and left half, leaving  .
On Saturday, he ate half and left half, leaving  .
The equation for all of this, since after Saturday morning there were 35 acorns left is this:
Multiply both sides by 64:
Subtract 32 from each side:
Check:
Add 2208 +32 = 2240 acorns on Monday afternoon. If Dale ate half on Monday, this leaves 1120 acorns on Monday night.
Tuesday = 560
Wednesday = 280
Thursday = 140
Friday = 70
Saturday = 35
It checks!!
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Hey, HERE'S AN EVEN BETTER WAY TO SOLVE THE ACORN PROBLEM, and it doesn't even require ALGEBRA!!
You can start with the acorns at the end of the week, which was 35 at the end of Saturday. Realizing that half were eaten each day, this means that at the beginning of Saturday, there were 35*2 = 70 acorns. Likewise at the beginning of each day, there would have been:
Saturday 35*2 = 70
Friday 70*2 = 140
Thursday = 140*2 = 280
Wednesday = 280*2 = 560
Tuesday = 560 *2 = 1120
Monday = 1120*2 = 2240
Now, undo the 32 acorns that they added on Monday before half were eaten (by subtracting!), and you have 2208 acorns to begin with.
R^2 at SCC
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