Solve the problem. Anne and Nancy use a metal alloy that is 24.9% copper to make jewelry. How many ounces of a 20% alloy must be mixed with a 27% alloy to form 100 ounces of the desired alloy?

.249*100=.20X+ .27(100-x)

solve for X

so then would it be 6 ounces of 20% alloy?

To solve this problem, we need to find the amount of each alloy needed to obtain the desired mixture.

Let's assume that x ounces of the 20% alloy will be mixed with y ounces of the 27% alloy to form 100 ounces of the desired alloy.

Since the percentage of copper in the 24.9% alloy is given, we know that the amount of copper in the final mixture should also be 24.9%.

The amount of copper in the 20% alloy can be calculated by multiplying the percentage of copper (20%) by the weight of the alloy (x ounces), giving us 0.2x ounces of copper.

Similarly, for the 27% alloy, the amount of copper can be calculated as 0.27y ounces.

As we want the final mixture to have 100 ounces of alloy and the total amount of copper should be 24.9% of 100 ounces, we can set up the equation:

0.2x + 0.27y = 0.249 * 100

Simplifying the equation:

0.2x + 0.27y = 24.9

Now, we need one more equation to solve the system of equations. Since the total amount of alloy in the final mixture is 100 ounces, we can write:

x + y = 100

Solving the system of equations using either substitution or elimination method, we can find the values of x and y.

Let's use the elimination method. Multiply the second equation by 0.2, so it becomes:

0.2x + 0.2y = 20

Now, subtract this equation from the first equation:

(0.2x + 0.27y) - (0.2x + 0.2y) = 24.9 - 20
0.07y = 4.9
y = 4.9 / 0.07
y ≈ 70

Substituting this value of y back into the second equation:

x + 70 = 100
x = 100 - 70
x = 30

Therefore, to form 100 ounces of the desired alloy, Anne and Nancy need to mix 30 ounces of the 20% alloy with 70 ounces of the 27% alloy.