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? 0.8(100 - x) + 0.6x = 100(0.65); 0.6(x) + 0.8(100 + x) = 0.65; 0.8(100) + 0.6x = 0.65(100 - x); 0.6(100 - x) + 0.8x = 100(0.65)

Explanation:

Step1: Define variables

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

Step2: Calculate copper from each mixture

The amount of copper from the 60% mixture is \( 0.6x \) (because 60% of \( x \) is copper). The amount of copper from the 80% mixture is \( 0.8(100 - x) \) (because 80% of \( 100 - x \) is copper).

Step3: Total copper in the final mixture

The total amount of copper in the 100 - pound mixture (which is 65% copper) is \( 100(0.65) \).

Step4: Set up the equation

The sum of the copper from the two mixtures should equal the copper in the final mixture. So, \( 0.8(100 - x) + 0.6x = 100(0.65) \).

Answer:

\( 0.8(100 - x) + 0.6x = 100(0.65) \)