Question

brass is made from a mixture of copper and other elements. a mixture that is 80% copper is combined with a mixture that is 60% copper, resulting in 100 pounds of brass that is 65% copper. which equation can be used to find x, the amount of 60% mixture used to create the 65% mixture? \\(\circ\\) \\(0.8(100 - x) + 0.6x = 100(0.65)\\) \\(\circ\\) \\(0.6(100 - x) + 0.8x = 100(0.65)\\) \\(\circ\\) \\(0.8(100) + 0.6x = 0.65(100 - x)\\) \\(\circ\\) \\(0.6(x) + 0.8(100 + x) = 0.65\\)

Explanation:

Step1: Define variables

Let \( x \) be the amount of 60% copper mixture. Then the amount of 80% copper mixture is \( 100 - x \) (since total mixture is 100 pounds).

Step2: Calculate copper from each mixture

• Copper from 80% mixture: \( 0.8(100 - x) \) (80% of \( 100 - x \) pounds).
• Copper from 60% mixture: \( 0.6x \) (60% of \( x \) pounds).
• Copper in final 65% mixture: \( 100(0.65) \) (65% of 100 pounds).

Step3: Set up the equation

The sum of copper from the two mixtures equals copper in the final mixture:
\( 0.8(100 - x) + 0.6x = 100(0.65) \)

Answer:

\( 0.8(100 - x) + 0.6x = 100(0.65) \) (the first option)