Question 152287: a stamp collection consists of 3, 8, 15, cent stamps. the number of 8 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 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, 15, cent stamps. the number of 8 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 stamps is 2.47. find the number of 8 cent stamps in the collection.
:
Let x, y, z = the quantity of 3, 8, & 15 cent stamps, respectively
:
Write an equation for each statement:
:
"the number of 8 stamps is one less than triple the number of 3 cent stamps."
y = (3x - 1)
;
"the number of 15 cent stamps is six less than the number of 8 cent stamps."
z = (y - 6)
:
" the total value of all stamps is 2.47."
.03x + .08y + .15z = 2.47
:
In the total value equation, replace z with (y-6)
.03x + .08y + .15(y-6) = 2.47
.03x + .08y + .15y - .9 = 2.47
.03x + .23y = 2.47 + .9
.03x + .23y = 3.37
;
In the above equation, replace y with (3x-1); find x:
.03x + .23(3x-1) = 3.37
.03x + .69x - .23 = 3.37
.72x = 3.37 + .23
.72x = 3.60
x = 
x = 5 ea 3 cent stamps
:
find the number of 8 cent stamps in the collection
y = 3x - 1
y = 3(5) - 1
y = 14 ea 8 cent stamps
;
:
Find the no. of 15 cent stamps so we can check the solutions in the total value eq
z = y - 6
z = 14 - 6
z = 8 ea 15 cent stamps
:
.03(5) + .08(14) + 8(.15) =
.15 + 1.12 + 1.20 = 2.47; confirms our solutions
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