Anne and Nancy use a metal alloy that is 20.45% copper to make jewelry. How many ounces of a 12% alloy must be mixed with a 25% alloy to form 100 ounces of the desired alloy?
amount of 12% stuff ---- x
amount of the other stuff ---- 100-x
solve for x:
.12x + .25(100-x) = .2045(100)
To solve this problem, we can use a basic algebraic approach. Let's assume that x represents the number of ounces of the 12% alloy that needs to be mixed, and y represents the number of ounces of the 25% alloy.
We are given the following information:
- The desired alloy is 100 ounces.
- The desired alloy contains 20.45% copper.
- The 12% alloy contains 12% copper.
- The 25% alloy contains 25% copper.
Now, let's set up two equations based on the copper content and the total amount of the alloy:
Equation 1: The copper content equation
0.12x + 0.25y = 0.2045(100)
Equation 2: The total amount equation
x + y = 100
We can now solve these equations simultaneously to find the values of x and y.
Step 1: Rearrange Equation 2 to solve for x:
x = 100 - y
Step 2: Substitute this value of x into Equation 1:
0.12(100 - y) + 0.25y = 0.2045(100)
Step 3: Simplify and solve for y:
12 - 0.12y + 0.25y = 20.45
0.13y = 8.45
y = 64.83
Step 4: Substitute the value of y back into Equation 2 to find x:
x = 100 - 64.83
x = 35.17
So, 35.17 ounces of the 12% alloy needs to be mixed with 64.83 ounces of the 25% alloy to form 100 ounces of the desired alloy.
To find the number of ounces of a 12% alloy and a 25% alloy needed to form 100 ounces of a desired alloy, we can set up an equation based on the amount of copper in each alloy.
Let's denote the number of ounces of the 12% alloy as "x" and the number of ounces of the 25% alloy as "100 - x" (since the total number of ounces is 100).
The equation can be formed based on the copper content:
0.12x + 0.25(100 - x) = 0.2045 * 100
Now, let's solve the equation to find the value of x:
0.12x + 25 - 0.25x = 20.45
-0.13x = -4.55
x = -4.55 / -0.13
x ≈ 35
Therefore, approximately 35 ounces of the 12% alloy should be mixed with (100 - 35) = 65 ounces of the 25% alloy to form 100 ounces of the desired alloy.