SOLUTION: Eight pounds of feathers and two ounces of gold together cost $932. Fourteen pounds of feathers and three ounces of gold together cost $1402. What is the cost of five pounds of fea

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Question 203388: Eight pounds of feathers and two ounces of gold together cost $932. Fourteen pounds of feathers and three ounces of gold together cost $1402. What is the cost of five pounds of feathers and five ounces of gold?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Eight pounds of feathers and two ounces of gold together cost $932. Fourteen pounds of feathers and three ounces of gold together cost $1402. What is the cost of five pounds of feathers and five ounces of gold?
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Equations:
8f + 2g = 932
14f + 3g = 1402
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Modify:
4f + g = 466
So, g = -4f + 466
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Substitute into the 2nd original equation to solve for "f":
14f + 3(-4f+466) = 1402
14f + -12f + 1398 = 1402
2f = 4
f = $2 per pound (price of feathers)
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Since g = -4f + 466 you get g = -4*2 + 466 = $458 per ounce (price of gold)
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What is the cost of five pounds of feathers and five ounces of gold?
5f + 5g = 5*2 + 5*458 = $2300
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Cheers,
Stan H.
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