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Puzzles Leftovers The Dunn family had several guests for Thanksgiving weekend. The menu for Thanksgiving dinner included turkey and candied yams (of course!) as well as orange rolls and pie. There was a lot of leftover food (except for the yams -- they disappeared quickly), making for good snacking all weekend. Each of the pies had been cut into six pieces, giving a total number of pie slices equal to the number of orange rolls initially baked by Mrs. Dunn. At Thanksgiving dinner on Thursday everyone ate two orange rolls and one slice of pie each. That night four of the guests left for home, but the next day everyone remaining at the house ate another orange roll and three more slices of pie each. As of Friday night, Mr. Dunn noted that there were still 7 orange rolls and two-thirds of a pie remaining.
Turkey sandwiches were also very popular fare that weekend. On Friday everyone in the house ate an equal number of turkey sandwiches. Two more guests left for home on Friday night. Then on Saturday everyone remaining at the house ate an equal number of turkey sandwiches, though they ate one fewer sandwich per person than they had eaten on Friday. Mr. Dunn calculated that there were eleven more sandwiches eaten on Friday than were eaten on Saturday.
Now, sort through all of that and tell me: how many turkey sandwiches were eaten at the Dunn house on Friday?
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Comments | terveloc |  23:36:00, 17 Nov 07 |  Newbie
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| 21 checks out
| | | | Jackson | 16:55:12, 09 Oct 07 | Newbie
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| I am pretty sure that it is 21.
Ok it is a system of equations, not an excel problem... And I also dont guess and check, its all algebra one
s=o
o-(g-4)-2g=7
s-3(g-4)-g =4
simplify to:
o-g+4-2g=7
s-3g+12-g=4
then to
o-3g=3
s-4g=-8
since o=s, we can multiply the second equation by -1 and substitute in the o and add em together
(o-3g) + -1(o-4g) = 3 + 8
o-3g -o +4g = 11
os cancel, and you add the gs
g=11
plug it in, and you get
o-7-22=7
o-29=7
o=36 (its divis by 6, good sign for pies)
now we have a little something to work with for part two. This is also a system of equations.
y=num eaten friday
x=rate eaten per person on friday
z=num eaten saturday
7x=y
5(x-1)=z
y=z+11, or y-11 = z
5x-5=y-11
5x+6=y
7x =y
change em out,
5x+6=7x
6=2x
x=3, plug it in for y:
5x+6=y
5*3 +6=y
15+6=y
y=21
and there ya go. Not hard to explain, so I am a bit more confident with my answer, and it did not rely on a computer to do it for me.
| | | | cosmo145 | 14:01:48, 09 Oct 07 | Newbie
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| 20 sandwiches were eaten on Friday.
I solved this using excel. There were 2 criteria I had to fill. One was that the total slices of pie be a multiple of 6 since they were cut into 6 Slices each, and nobody bakes less than a whole pie.
Secondly the difference between Saturday and Friday was 11 sandwiches.
By first setting the guests left on Saturday so that the initial pies = a multiple of 6 I could then change the number of sandwiches eaten on Saturday until I got a difference of 11 between the 2 days.
This is more difficult than I thought to explain...
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