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
Question 176649: 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 ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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.
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let x = no. of 3 ct stamps
let y = no. of 8 ct
let z = no. of 15 ct
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write an equation for each statement:
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" The number of 8 cent stamps is one less than triple the number of 3 cent stamps."
y = 3x - 1
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" The number of 15 cent stamps is six less than the number of 8 cent stamps."
z = y - 6
put z in terms of x also; substitute (3x-1) for y
z = (3x-1) - 6
z = 3x - 7
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The total value of all the stamps is $2.47.
.03x + .08y + .15z = 2.47
substitute for y & z
.03x + .08(3x-1) + .15(3x-7) = 2.47
:
.03x + .25x - .08 + .45x - 1.05 = 2.47
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.03x + .25x - .45x - .08 - 1.05 = 2.47
:
.72x - 1.13 = 2,47
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.72x = 1.13 + 2.47
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.72x = 3.60
x =
x = 5 ea 3 ct stamps
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Find the number of 8 cent stamps in the collection.
y = 3x -1
y = 3(5) - 1
y = 14 ea 8 ct stamps
:
:
check solution
z = 14-6 = 8 ea 15 ct stamps
.03(5) + .08(14) + .15(8) = 2.47
.15 + 1.12 + 1.20 = 2.47; confirms our solutions
