SOLUTION: You need to purchase 100 stamps and only spend $100. Using only .25, $1, $15 stamps, and you need to buy at least one of each type of stamp, how many of each stamp do you buy?

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Question 261355: You need to purchase 100 stamps and only spend $100. Using only .25, $1, $15 stamps, and you need to buy at least one of each type of stamp, how many of each stamp do you buy?
Thank you for your help!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You need to purchase 100 stamps and only spend $100. Using only .25, $1, $15 stamps, and you need to buy at least one of each type of stamp, how many of each stamp do you buy?

system%28x%2By%2Bz=100%2C%0D%0A.25x%2By%2B15z=100%2C%0D%0Ax%3E=1%2C+y%3E=1%2Cz%3E=1%29

Solve the two equations for x and y in terms of z:

system%28x=%2856%2F3%29z%2Cy=100-%2859%2F3%29z%2C+x%3E=1%2C+y%3E=1%2Cz%3E=1%29

So z must be a multiple of 3 in order for x and y to be integers. 

Since y%3E=1,

100-%2859%2F3%29z%3E=1
300-59z%3E=3
-59z%3E=-297
z%3C=297%2F59
z%3C=5%262%2F59

1+%3C=+z+%3C=+5

And the only multiple of 3 between 1 and 5 is 3.

So z must be 3

So x=%2856%2F3%29z=%2856%2F3%29%2A3=56

and y=100-%2859%2F3%29z+=+100-%2859%2F3%29%283%29=100-59=41

So the only solution is 56 $.25 stamps, 41 $1 stamps and 3 $15 stamps.

Edwin