SOLUTION: A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less t

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Question 173305: A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is $2.47. Find the number of 8 cent stamps in the collection
Answer by solver91311(24713) About Me  (Show Source):
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Let n be the number of 3 cent stamps, then the number of 8 cent stamps has to be 3n-1, and then the number of 15 cent stamps is %283n-1%29-%286%29=3n-7

The value of the 3 cent stamps, in cents, is 3n

The value of the 8 cent stamps, in cents, is 8%283n-1%29=24n-8

The value of the 15 cent stamps, in cents, is 15%283n-7%29=45n-105

The sum of these values is $2.47, or expressed in cents, 247 cents, so you can write:

3n%2B24n-8%2B45n-105=247

Simplified:

72n-113=247

72n=360

n=5.

So there are five 3-cent stamps. I'll leave it to you to figure out how many 8 and 15 cent stamps based on knowing there are five 3-cent stamps. You should also check the work to make sure your answers fulfill the requirements of the problem statement.