anne and nancy use a metal alloy that is 19.3% copper to make jewelry. how many ounces of a 19% alloy must be mixed with a 20% alloy to form 110 ounces of the desired alloy?
110*.193=X*.19+(110-x).20
solve for X.
To determine the number of ounces of the 19% alloy and the 20% alloy needed to form the desired alloy, we can set up a system of equations based on the given information.
Let's assume that x represents the number of ounces of the 19% alloy and y represents the number of ounces of the 20% alloy.
Since the desired alloy is 110 ounces, we know that x + y = 110. This is our first equation.
We also know that the 19% alloy consists of 19.3% copper. So, 0.193x ounces of copper will come from the 19% alloy.
Similarly, the 20% alloy consists of 20% copper. Thus, 0.20y ounces of copper will come from the 20% alloy.
In the desired alloy, the total amount of copper will be x + y ounces. And since the desired alloy is 19.3% copper, we have the equation:
0.193x + 0.20y = 0.193 * 110
Simplifying this, we get:
0.193x + 0.20y = 21.23
Now we have a system of equations:
x + y = 110
0.193x + 0.20y = 21.23
To solve this system, we can use either substitution or elimination method. Let's use the substitution method here.
From the first equation, we have x = 110 - y.
Substituting x in the second equation, we get:
0.193(110 - y) + 0.20y = 21.23
Simplifying this equation, we get:
21.23 - 0.193y + 0.20y = 21.23
Combining like terms, we have:
0.007y = 0
Dividing both sides of the equation by 0.007, we find:
y = 0
This indicates that there is no need for any ounces of the 20% alloy to be mixed in. Therefore, the entire 110 ounces must consist of the 19% alloy.
Hence, Anne and Nancy must use 110 ounces of the 19% alloy to make the desired alloy.