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 than

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Question 154176: 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. Please help me with this problem I am having a difficult time with it.Thank you
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of 3 cent stamps.
Then the number of 8 cent stamps is 3x - 1.
The number of 15 cent stamp is (3x - 1) - 6 = 3x - 7
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The value of the 3 cent stamps is 3x.
The value of the 8 cent stamps is 8(3x - 1).
The value of the 15 cent stamps is 15(3x - 7).
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The total value is 3x + 8(3x - 1) + 15(3x - 7)
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As the total value is $2.47 = 247 cents, we have
3x + 8(3x - 1) + 15(3x - 7) = 247
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Solving the equation for x, we obtain:
3x + 24x - 8 + 45x - 105 = 247
72x - 113 = 247
72x = 360
x = 5.
So
the number of 3 cent stamps is 5.
the number of 8 cent stamps is 3x - 1 = 3*5 - 1 = 14.
the number of 15 cent stamps is 3x - 7 = 3*5 - 7 = 8