SOLUTION: Anne and Nancy use a metal alloy that is 19.75% copper to make jewalry. How many ounces of an 18% alloy must be mixed with a 21% alloy to form 108 ounces of the desired alloy?

Question 146437: Anne and Nancy use a metal alloy that is 19.75% copper to make jewalry. How many ounces of an 18% alloy must be mixed with a 21% alloy to form 108 ounces of the desired alloy?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Anne and Nancy use a metal alloy that is 19.75% copper to make jewalry. How many ounces of an 18% alloy must be mixed with a 21% alloy to form 108 ounces of the desired alloy?
.
Let x = ounces of 18% copper
and y = ounces of 21% copper
.
since we have two unknowns, we need two equations.
.
from:"use a metal alloy that is 19.75% copper" we get equation 1:
.18x + .21y = 19.75
.
from:"form 108 ounces of desired alloy" we get equation 2:
x + y = 108
.
Solve equation 2 for x we get:
x + y = 108
x = 108 - y
.
Substitute this into equation 1 and solve for y:
.18x + .21y = 19.75
.18(108 - y) + .21y = 19.75
.18(108 - y) + .21y = 19.75
19.44 - .18y + .21y = 19.75
19.44 + .03y = 19.75
.03y = .31
y = 10.3333 (10 and 1/3) ounces
.
substitute the above into equation 2 and solve for x:
x + y = 108
x + 10.333 = 108
x = 108 - 10.333
x = 97.667 (97 and 2/3) ounces

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