Final answer:
To create an alloy containing 38% silver from a metal containing 30% silver and another containing 50% silver, 12 mg of the 30% silver metal must be mixed with 8 mg of the 50% silver metal.
Step-by-step explanation:
To determine how many milligrams (mg) of a metal containing 30% silver must be combined with 8 mg of a metal containing 50% silver to form an alloy containing 38% silver, we can set up an equation based on the mass of silver in each component. Let's denote the mass of the metal containing 30% silver needed as x mg.
The amount of silver from the 30% metal is 0.30x, and the amount of silver from the 8 mg 50% metal is 0.50×8 = 4 mg. The total mass of the alloy is x + 8 mg and the total amount of silver in the alloy should be 0.38(x + 8). Setting up the equation:
0.30x + 4 = 0.38(x + 8)
Solving for x gives:
0.30x + 4 = 0.38x + 3.04
0.08x = 0.96
x = 12 mg
Therefore, 12 mg of the metal containing 30% silver is needed to be combined with the 8 mg of the metal containing 50% silver.