Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Sure, let's go through the problem step-by-step to find the value of [tex]\( x \)[/tex], the acid concentration of the first solution.
1. Given Information:
- We have 4 liters of one acid solution with an unknown concentration [tex]\( x \)[/tex].
- We have 10 liters of a 40% acid solution.
- The final mixture is 14 liters with a 30% acid concentration.
2. Set Up the Equation:
To find [tex]\( x \)[/tex], we will set up an equation based on the amount of pure acid in each solution.
The amount of pure acid in the first solution is [tex]\( 4 \times x \)[/tex].
The amount of pure acid in the 40% solution is [tex]\( 10 \times 0.40 = 4 \)[/tex] liters.
The amount of pure acid in the final mixture is [tex]\( 14 \times 0.30 = 4.2 \)[/tex] liters.
3. Form the Equation:
We know that the total amount of acid in the mixture is the sum of the amounts of pure acid from each solution. So, we set up the following equation:
[tex]\[ 4x + 4 = 4.2 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 4 = 4.2 \][/tex]
Subtract 4 from both sides:
[tex]\[ 4x = 0.2 \][/tex]
Divide by 4:
[tex]\[ x = \frac{0.2}{4} = 0.05 \][/tex]
So, the concentration of the first solution is [tex]\( 5\% \)[/tex].
Thus, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{0.05} \)[/tex].
1. Given Information:
- We have 4 liters of one acid solution with an unknown concentration [tex]\( x \)[/tex].
- We have 10 liters of a 40% acid solution.
- The final mixture is 14 liters with a 30% acid concentration.
2. Set Up the Equation:
To find [tex]\( x \)[/tex], we will set up an equation based on the amount of pure acid in each solution.
The amount of pure acid in the first solution is [tex]\( 4 \times x \)[/tex].
The amount of pure acid in the 40% solution is [tex]\( 10 \times 0.40 = 4 \)[/tex] liters.
The amount of pure acid in the final mixture is [tex]\( 14 \times 0.30 = 4.2 \)[/tex] liters.
3. Form the Equation:
We know that the total amount of acid in the mixture is the sum of the amounts of pure acid from each solution. So, we set up the following equation:
[tex]\[ 4x + 4 = 4.2 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 4 = 4.2 \][/tex]
Subtract 4 from both sides:
[tex]\[ 4x = 0.2 \][/tex]
Divide by 4:
[tex]\[ x = \frac{0.2}{4} = 0.05 \][/tex]
So, the concentration of the first solution is [tex]\( 5\% \)[/tex].
Thus, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{0.05} \)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.