Question 169683
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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