SOLUTION: Samuel has an alloy containing 11% gold. Taylor has 1/2 ounces of an alloy containing 70% gold. They combined their alloys to make an alloy with 36 2/7% gold. Gold is worth $388.31
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Question 486830: Samuel has an alloy containing 11% gold. Taylor has 1/2 ounces of an alloy containing 70% gold. They combined their alloys to make an alloy with 36 2/7% gold. Gold is worth $388.31 an ounce at the current market value. Samuel estimated the value of the new alloy to be $164.38 an ounce. How many ounces of Samuel's alloy were used?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Samuel has an alloy containing 11% gold.
Taylor has 1/2 ounces of an alloy containing 70% gold.
They combined their alloys to make an alloy with 36 2/7% gold.
Gold is worth $388.31 an ounce at the current market value.
Samuel estimated the value of the new alloy to be $164.38 an ounce.
How many ounces of Samuel's alloy were used
:
Change 36 to 36.2857%
:
Let x = amt of Sam's alloy used
:
.11x + .70(.5) = .362857(x+.5)
:
.11x + .35 = .362857x + .18143
:
.35 - .18143 = .362857x - .11x
:
.16857 = .252857x
x =
x = .667 oz of 11% alloy
:
Check this using the values given
.362857(.6667+.5) = .4233 oz of gold
Find the value
.4233 * 388.31 = $164.37, which is within 1 cent
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