Anne and Nancy use a metal alloy that is 23.5% copper to make jewelry. How many ounces of a
21% alloy must be mixed with a 30% alloy to form 108 ounces of the desired alloy?
you want the final 108 oz to be 23.5% copper. That means it contains 25.38 oz of copper
So, if there are x oz of 21% alloy,
.21x + .30(108-x) = .235(108)
.21x + 32.4 - .30x = 25.38
.09x = 7.02
x = 78
so, she uses 78 oz of 21% and 30 oz of 30%
To solve this problem, we can set up an equation based on the amount of copper in the alloys.
Let's assume x ounces of the 21% alloy is mixed with y ounces of the 30% alloy.
According to the problem, the final alloy should contain 108 ounces of copper. Therefore, we can write the equation:
0.21x + 0.3y = 0.235(108)
Simplifying the equation:
0.21x + 0.3y = 25.38
Next, we need to consider the total amount of alloy in the mixture, which is 108 ounces. So we can write the equation:
x + y = 108
To solve these equations, we can use the method of substitution or elimination.
Let's solve by substitution:
Rearrange the second equation to x = 108 - y.
Substitute this value into the first equation:
0.21(108 - y) + 0.3y = 25.38
22.68 - 0.21y + 0.3y = 25.38
Combine like terms:
0.09y = 2.7
Divide both sides by 0.09:
y = 30
Now substitute the value of y back into the second equation to find x:
x + (30) = 108
x = 78
Therefore, you would need 78 ounces of the 21% alloy mixed with 30 ounces of the 30% alloy to form 108 ounces of the desired alloy.
To solve this problem, we need to use the concept of the mixture equation. Let's break down the problem step by step:
Let's assume that x ounces of the 21% alloy are used.
Since we want to have a total of 108 ounces of the desired alloy, the remaining amount will be (108 - x) ounces.
In the 21% alloy, we know that 21% of the total weight contains copper. So, 0.21x ounces of copper are present in the 21% alloy.
Similarly, in the 30% alloy, 0.30(108 - x) ounces of copper are present.
The total amount of copper in the mixture should be equal to 23.5% of the total weight, which is 0.235(108) ounces.
Now, we can create an equation to solve for x:
0.21x + 0.30(108 - x) = 0.235(108)
Let's simplify and solve for x:
0.21x + 32.4 - 0.30x = 25.38
Combining like terms:
-0.09x + 32.4 = 25.38
Moving constants to the other side:
-0.09x = 25.38 - 32.4
-0.09x = -7.02
Now, divide both sides by -0.09:
x = (-7.02) / (-0.09)
x ≈ 78
So, approximately 78 ounces of the 21% alloy should be mixed with (108 - 78) = 30 ounces of the 30% alloy to form 108 ounces of the desired alloy.