SOLUTION: A stamp collection consisits of 5, 13,and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. The number of 18 cent stamps is five more
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Question 81234: A stamp collection consisits of 5, 13,and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. The number of 18 cent stamps is five more than the number of 13 cent stamps. The total value of all the stamps is $2.60. Find the number of 13 cent stamps in the collection. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Write an equation for each statement.
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A stamp collection consists of 5, 13,and 18 cent stamps.
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x = no of 5 cent stamps; y = 13 cent stamps; z = 18 cent stamps
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The number of 13 cent stamps is one less than twice the number of 5 cent stamps.
y = 2x - 1
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The number of 18 cent stamps is five more than the number of 13 cent stamps.
z = y + 5
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The total value of all the stamps is $2.60.
.05x + .13y + .18z = 2.60
Get rid of the decimals; multiply equation by 100
5x + 13y + 18z = 260
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Find the number of 13 cent stamps in the collection.
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put x in terms of y also;
y = 2x - 1
-2x = -y - 1
2x = y + 1
x = .5y + .5
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Substitute for x and z in the total equation
5x + 13y + 18z = 260
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5(.5y+.5) + 13y + 18(y+5) = 260
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2.5y + 2.5 + 13y + 18y + 90 = 260
2.5y + 13y + 18y = 260 - 2.5 - 90
33.5y = 167.5
y = 167.5/33.5
y = 5 ea 13 cent stamps
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In order to check the solution, find x and z and substitute in the total eq;
I'll let you do that.
