SOLUTION: A chemist is studying the properties of a bronze alloy (mixture) of copper and tin. She begins with 10 kg of an alloy that is one fifth tin. Keeping the amount of copper constant,

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Question 169683This question is from textbook Wiley: Functions Modeling Change: A Preparation for Calculus
: A chemist is studying the properties of a bronze alloy (mixture) of copper and tin. She begins with 10 kg of an alloy that is one fifth tin. Keeping the amount of copper constant, she adds small amounts of tin to the alloy. Letting x be the total amount of tin added, define
C(x) = Concentration of tin = Total amount of tin/Total amount of alloy

Find a formula for C(x)
 This question is from textbook Wiley: Functions Modeling Change: A Preparation for Calculus

Found 2 solutions by stanbon, gonzo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A chemist is studying the properties of a bronze alloy (mixture) of copper and tin.
She begins with 10 kg of an alloy that is one fifth tin.
Keeping the amount of copper constant, she adds small amounts of tin to the alloy.
Letting x be the total amount of tin added, define
C(x) = Concentration of tin = Total amount of tin/Total amount of alloy
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C(x) = [(1/5)(10kg)+x]/[10 + x]
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Cheers,
Stan H.

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
she starts off with 10 kg of alloy.
this is composed of 4/5 bronze and 1/5 tin
bronze = 4/5 * 10 = 8 kg
tin = 1/5 * 10 = 2 kg
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she adds x amount of tin to the alloy.
new amount of tin = 2 + x
new amount of alloy = 10 + x
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concentration is defined as amount of tin divided by total amount of alloy.
formula for concentration of tin is:
C(x) = (2+x)/(10+x)
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here's how it works:
original concentration has x = 0, so
C(x) = (2+x)/(10+x) becomes:
C(0) = 2/10 = .2 = 1/5 which is the original concentration.
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if x is anything greater than 0 measured in kilograms, she will have a new concentration as follows:
C(x) = (2+x) / (10 + x)
if we assume the amount of tin doubles, then x would equal to 2.
the equation becomes:
C(2) = (2+2) / (10 + 2)
which simplifies as follows:
C(2) = (4) / (12) = 1/3 = .333333333.....
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