Connect with a community of experts and enthusiasts on IDNLearn.com. Ask any question and receive timely, accurate responses from our dedicated community of experts.
Sagot :
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.
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.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.