Question 974845: Cookies are sold singly or in packages of 13 or 39. With this packaging, how many ways can you buy 78 cookies?
Found 3 solutions by Edwin McCravy, Alan3354, Jelly6584:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! Cookies are sold singly or in packages of 13 or 39.
With this packaging, how many ways can you buy 78 cookies?
Just by trial and error you can easily get the answer
1. 2 boxes of 39,
2. 1 box of 39 and 2 boxes of 13, and
3. 6 boxes of 13.
If you're supposed to use algebra or number theory, then
Let x = the number of packages of 13 cookies
Let y = the number of packages of 39 cookies.
That leads to the Diophantine equation:
13x + 39y = 78
Divide through by 13
x + 3y = 6
x = 6 - 3y
x ≥ 0, y ≥ 0
6 - 3y ≥ 0
-3y ≥ -6
y ≤ 2
Also y ≥ 0 so
0 ≤ y ≤ 2
Since y is an integer, y can only take on the values 0,1, and 2.
So the answer is 3.
They are 2 boxes of 39,
1 box of 39 and 2 boxes of 13, and
6 boxes of 13.
Edwin
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Cookies are sold singly or in packages of 13 or 39. With this packaging, how many ways can you buy 78 cookies?
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The other tutor is wrong.
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You can buy 78 singles.
--> 78 1's
6 13's
2 39's
-------
1 39 and 3 13's
1 39, 2 13's and 13 1's
1 39, 1 13 and 26 1's
1 39 and 39 singles
----
1 13 and 65 singles
2 13's and 52 singles
3 13's and 39 singles
4 13's and 26 singles
5 13's and 13 singles
Answer by Jelly6584(1)  (Show Source):
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