What are the values of the remaining stamps?

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Homework Help Overview

The problem involves determining the values of two stamp denominations given that there are exactly 33 postage amounts that cannot be formed, including the amount of 46 cents. The context suggests a focus on combinations of these stamp values to create various postage amounts, with a specified range from 1 to 100 cents.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of the equation ax + by = 46, noting the possibility of negative solutions. There are questions regarding the common factors of the two stamp values and how they relate to the maximum value that cannot be formed. Ambiguities about the interpretation of the problem statement regarding the role of 46 cents are also raised.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions made about the values of the stamps. Some guidance has been offered regarding the mathematical relationships involved, but no consensus has been reached on the specifics of the stamp values.

Contextual Notes

There is ambiguity in the problem statement regarding whether 46 cents is one of the stamp values or one of the amounts that cannot be formed. This uncertainty may affect the approach to finding the solution.

jaqueh
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Homework Statement


There are exactly 33 postage amounts that cannot be made up using these stamps, including 46 cents. What are the values of the remaining stamps?

Homework Equations


stamp 1 = x
stamp 2 = y
Im assuming postage amounts range from 1 to 100 cents

The Attempt at a Solution


ax+by=46 has a negative solution obviously. So either a or b < 0. I cannot get any farther than that.
 
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I take it there are only two stamp values.
Can you say anything about common factors of x and y?
Can you then determine the max value that cannot be made from them?
 
jaqueh said:

Homework Statement


There are exactly 33 postage amounts that cannot be made up using these stamps, including 46 cents. What are the values of the remaining stamps?
I find this ambiguous. Is one of the stamps 46 cents or is one of the "postage amounts that cannot be made up" 46 cents?

Homework Equations


stamp 1 = x
stamp 2 = y
Im assuming postage amounts range from 1 to 100 cents

The Attempt at a Solution


ax+by=46 has a negative solution obviously. So either a or b < 0. I cannot get any farther than that.[/QUOTE]
 
HallsofIvy said:
I find this ambiguous. Is one of the stamps 46 cents or is one of the "postage amounts that cannot be made up" 46 cents?
Having solved it on the assumption that it means 46c cannot be made up, I'm pretty sure that's what is intended.
 

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