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Amy uses 48-cent stamps and 7-cent stamps to mail a gift card to a friend. If the postage is $2.07, how many of each stamp did Amy use?

User Pratap Koritala
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1 Answer

21 votes
21 votes

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Answer:

3 48-cent stamps

9 7-cent stamps

Explanation:

The number of 48-cent stamps Amy can use is less than 207/48 ≈ 4.3, so we can find the numbers by trial and error. We want ...

48a +7b = 207 . . . . . . postage in cents, where a, b are the numbers of stamps

b = (207 -48a)/7 = 29 4/7 -a(7 -1/7) = (29 -7a) +(a+4)/7

In order for b to be an integer, we must have (a+4) a multiple of 7. The least value of 'a' that will make this true is a=3. That value gives ...

b = (29 -7·3) +(3+4)/7 = 8 +1 = 9

Amy used 3 48-cent stamps and 9 7-cent stamps.

User Dave Ankin
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