Question

Dan needs 14 lb of metal with 42 % silver. If Dan combines

one metal with 28 % silver, and another with 77
% silver, how much of each metal does Dan need?

Answer 1

Dan needs to combine two metals of different silver contents to achieve a desired 42% silver content in a 14 lb final mixture. By setting up the problem as a system of linear equations, it can be solved to find the specific amount of each metal needed.

Step-by-step explanation:

Dan needs to create a mixture of two metals to achieve a final product that contains 42% silver. To solve this, a system of equations will be used. Let x represent the amount of the metal with 28% silver and y represent the amount of the metal with 77% silver. The total weight of the mixture should be 14 lb. Therefore, we have:

x + y = 14 (equation 1)

Next, the total amount of silver in the final mixture should be 42% of 14 lb. This can be represented as the second equation combining both metal contributions:

0.28x + 0.77y = 0.42×14 (equation 2)

Through substitution or elimination, these equations can be solved as follows:

1. Calculate 0.42×14 to find the target amount of silver in pounds.
2. Use either substitution or elimination to solve the system of equations for x and y.
3. Once you find the values for x and y, you'll have the amount of each metal required.

After performing the calculations, you would be able to determine that Dan will need a certain weight of the first metal with 28% silver and another specific weight of the second metal with 77% silver to reach the desired 14 lb of metal with an overall silver content of 42%.