Question 205122: Can someone please help me with this problem?
A package is 12 inches longer than it is wide. It is also 6 inches wider than it is high. If the total length of the ribbon needed to go around both ways is 96 inches long. What is the length of the package?
Answer by Theo(13342)   (Show Source):
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Your answer is:
length of the package is 24 inches
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Here's how it was found.
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length of your package is represented by the lines:
AB, DC, HG, and EF
also R2AR2B and R2DR2C
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width of your package is represented by the lines:
AD, BC, FG, EH
also R1AR1B and R1DR1C
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the height of your package is represented by the lines:
AE, BF, CG, DH
also R1AR1D, R1BR1C, R2BR2C, R2AR2D
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Your first ribbon is R1 and it goes around 2 times the height and 2 times the width.
Your second ribbon is R2 and it goes around 2 times the height and 2 times the length.
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your height = H
your width = W = H+6
your length = L = W+12
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R1 + R2 = 96 inches.
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R1 = 2H + 2W
R2 = 2H + 2L
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Since W = H+6, then:
R1 = 2H + 2(H+6) = 2H + 2H + 12 = 4H + 12
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Since L = W + 12 and W = H + 6 then:
L = (H+6) + 12 = H + 18 and:
R2 = 2H + 2L = 2H + 2*(H+18) = 2H + 2H + 36 = 4H + 36
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We have:
R1 = 4H + 12
R2 = 4H + 36
R1 + R2 = 96
4H + 12 + 4H + 36 = 96
combine like terms to get:
8H + 48 = 96
subtract 48 from both sides to get:
8H = 48
divide both sides by 8 to get:
H = 6
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We have H = 6
W = H + 6 so W = 12
L = W + 12 so L = 24
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H = 6
W = 12
L = 24
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going back to the ribbons.
R1 = 2H + 2W = 2*6 + 2*12 = 12 + 24 = 36 inches.
R2 = 2H + 2L = 2*6 + 2*24 = 12 + 48 = 60 inches.
R1 + R2 = 36 + 60 = 96 inches.
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Everything checks out so the length of your package = L = 24 inches.
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