Answered

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 [tex]\( x \)[/tex], the amount of 60% mixture used to create the 65% mixture?

A. [tex]\(0.8(100 - x) + 0.6x = 100(0.65)\)[/tex]

B. [tex]\(0.8(100) + 0.6x = 0.65(100 - x)\)[/tex]



Answer :

GinnyAnswer
Certainly! To find the amount of the 60% mixture used to create the final 65% mixture, we need to set up the equation based on the information provided.

Let's break it down step-by-step.

1. Define the variables:
- Let [tex]\( x \)[/tex] be the amount of the 60% copper mixture (in pounds).
- Since the total weight of the final mixture is 100 pounds, the amount of the 80% copper mixture will be [tex]\( 100 - x \)[/tex] pounds.

2. Set up the equation:

The total amount of copper contributed by each mixture should equal the amount of copper in the final mixture.

- From the 80% copper mixture:
[tex]\[ 0.8 \times (100 - x) \][/tex]
Here, [tex]\( 0.8 \)[/tex] represents the 80% copper content, and [tex]\( 100 - x \)[/tex] is the amount of the 80% mixture.

- From the 60% copper mixture:
[tex]\[ 0.6 \times x \][/tex]
Here, [tex]\( 0.6 \)[/tex] represents the 60% copper content, and [tex]\( x \)[/tex] is the amount of the 60% mixture.

- The amount of copper in the final 65% mixture:
[tex]\[ 0.65 \times 100 \][/tex]
Since the final mixture weighs 100 pounds with 65% copper content.

3. Combine these into a single equation:
[tex]\[ 0.8(100 - x) + 0.6x = 100 \times 0.65 \][/tex]

So the equation properly set up to find [tex]\( x \)[/tex] is:
[tex]\[ 0.8(100 - x) + 0.6x = 100 \times 0.65 \][/tex]

You can solve this equation to find the value of [tex]\( x \)[/tex], the amount of the 60% copper mixture used.

Other Questions