SOLUTION: A stamp collection consists of 3,8, and 15 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 th

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Question 150545: A stamp collection consists of 3,8, and 15 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 mangopeeler07(462) About Me  (Show Source):
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A stamp collection consists of 3,8, and 15 cent stamps.
x=# 3 cent stamps
y=# 8 cent stamps
z=# 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.
y=3x-1
z=3x-1-6

The total value of all the stamps is $2.47.
3x+8y+15z=247

PLug in values for y and z
3x+8(3x-1)+15(3x-7)=247

Distribute
3x+24x-8+45x-105

Combine like terms
72x-113=247

Add 113 to both sides
72x=360

Divide both sides by 72
x=5

5 3cent stamps
y=3x-1

y=3(5)-1
y=14
14 8 cent stamps

z=3x-7
z=3(5)-7
z=8
8 15 cent stamps

Answer:
# 3 cent stamps= 5
# 8 cent stamps= 14
# 15 cent stamps= 8