On the last day of his vacation, a man goes into a gift shop to buy presents for his grandchildren.
arithmetic/knapsacks New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
On the last day of his vacation, a man goes into a gift shop to buy presents for his grandchildren. There he finds 45 brightly colored knapsacks, 15 in each of three styles. The three kinds of knapsacks are priced at $16.67, $16.72 and $17.52, including tax. The man chooses some of the knapsacks and pays for them in exact change with one or more $50 traveler's checks and exactly one dollar bill. How many of each kind did he buy?
Show solution
12 * $16.67 = $200.04
+ 2 * 16.72 = 33.44
+ 17.52 = 17.52
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$251.00 = 5 $50 Travelor's Checks + $1 bill.
In article <D2HyBs.5E2@tc.fluke.com>, Gary Benson <inc@tc.fluke.COM>
wrote:
>So how did you arrive at your answer?
Ok. My approach involved seeing how the 3 values differed from the
average. Let's first assume we could do the whole thing with just one
$50 traveler's check + the $1 bill:
$16.67 $16.72 $17.52
(.33 too low) (.28 too low) (.52 too high)
They add up to $.09 too low.
At this point, we have to use different averages, since we're only
adding $50 for each try. So now we have to compare the values against
not $17.00 exactly, but $16.66 + 2/3:
$16.67 $16.72 $17.52
(1/3 too high, 5 1/3 too high, 85 1/3 too high -- I'm counting
cents)
It's pretty clear (at least to me), that we won't be counting the 3rd
figure any more. So if we count the 1st figure twice, that's
2/3 + 5 1/3 = 6 too high, which brings us from 9 too low to only 3 too
low. Now we won't be using the 2nd figure anymore either. All we need
is 9 more counts of the 1st figure and we're done!
So how many of the 1st figure did we use? 1 + 2 + 9 = 12
" " " 2nd " " " 1 + 1 = 2
" " " 3rd " " " 1 = 1
And that's how I got the answer!
-- Jim Waters <jiwaters@nyx10.cs.du.edu>