IDNLearn.com helps you find the answers you need quickly and efficiently. Our community provides timely and precise responses to help you understand and solve any issue you face.
Sagot :
Alright Eli, let's work through this step by step and complete the table you have.
First, let's define what we have and need to find using the variables given:
1. 10% Acetic Acid Solution
- Volume: [tex]\(0.5\)[/tex] gallons
- Concentration: [tex]\(10\%\)[/tex] (or 0.10)
2. 35% Acetic Acid Solution
- Volume: [tex]\(v\)[/tex] gallons
- Concentration: [tex]\(35\%\)[/tex] (or 0.35)
3. Mixture
- Desired Concentration: [tex]\(15\%\)[/tex] (or 0.15)
- Total Volume: [tex]\(v + 0.5\)[/tex] gallons
Now, let's calculate the amounts as requested and complete the table. Here's the additional information needed for calculations:
- The amount of acetic acid in the [tex]\(10\%\)[/tex] solution is:
[tex]\[ 0.5 \text{ gallons} \times 0.10 = 0.05 \text{ gallons of acetic acid} \][/tex]
- The amount of acetic acid in the [tex]\(35\%\)[/tex] solution is:
[tex]\[ 0.35 v \text{ gallons of acetic acid} \][/tex]
- The total volume of the mixture:
[tex]\[ v + 0.5 \text{ gallons} \][/tex]
- The amount of acetic acid in the mixture:
[tex]\[ 0.15 (v + 0.5) \text{ gallons of acetic acid} \][/tex]
Given that we want the total amount of acetic acid in the mixture to be the sum of the amount from the [tex]\(10\%\)[/tex] and [tex]\(35\%\)[/tex] solutions, we can set up the equation:
[tex]\[ 0.05 + 0.35 v = 0.15 (v + 0.5) \][/tex]
From the values calculated:
[tex]\[ v = 0.125 \text{ gallons} \][/tex]
Now, let's fill out the required table with these values:
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{c}
Amount of \\
Solution
\end{tabular} & \begin{tabular}{c}
Acid \\
Concentration
\end{tabular} & \begin{tabular}{c}
Amount of \\
Acid
\end{tabular} \\
\hline
[tex]$10\%$[/tex] Acid & [tex]$0.5$[/tex] gal & [tex]$0.10$[/tex] & [tex]$(0.10)(0.5) = 0.05$[/tex] \\
\hline
[tex]$35\%$[/tex] Acid & [tex]$v = 0.125$[/tex] gal & [tex]$0.35$[/tex] & [tex]$0.35 (0.125) = 0.04375$[/tex] \\
\hline
Mixture & [tex]$v + 0.5 = 0.625$[/tex] gal & [tex]$0.15$[/tex] & [tex]$0.15 (0.625) = 0.09375$[/tex] \\
\hline
\end{tabular}
So, the filled table is:
> \begin{tabular}{|c|c|c|c|}
> \hline & \begin{tabular}{c}
> Amount of \\
> Solution
> \end{tabular} & \begin{tabular}{c}
> Acid \\
> Concentration
> \end{tabular} & \begin{tabular}{c}
> Amount of \\
> Acid
> \end{tabular} \\
> \hline [tex]$10\%$[/tex] Acid & [tex]$0.5$[/tex] gal & [tex]$0.10$[/tex] & [tex]$0.05$[/tex] \\
> \hline [tex]$35\%$[/tex] Acid & [tex]$0.125$[/tex] gal & [tex]$0.35$[/tex] & [tex]$0.04375$[/tex] \\
> \hline Mixture & [tex]$0.625$[/tex] gal & [tex]$0.15$[/tex] & [tex]$0.09375$[/tex] \\
> \hline
> \end{tabular}
This table now accurately represents the given problem and the quantities involved.
First, let's define what we have and need to find using the variables given:
1. 10% Acetic Acid Solution
- Volume: [tex]\(0.5\)[/tex] gallons
- Concentration: [tex]\(10\%\)[/tex] (or 0.10)
2. 35% Acetic Acid Solution
- Volume: [tex]\(v\)[/tex] gallons
- Concentration: [tex]\(35\%\)[/tex] (or 0.35)
3. Mixture
- Desired Concentration: [tex]\(15\%\)[/tex] (or 0.15)
- Total Volume: [tex]\(v + 0.5\)[/tex] gallons
Now, let's calculate the amounts as requested and complete the table. Here's the additional information needed for calculations:
- The amount of acetic acid in the [tex]\(10\%\)[/tex] solution is:
[tex]\[ 0.5 \text{ gallons} \times 0.10 = 0.05 \text{ gallons of acetic acid} \][/tex]
- The amount of acetic acid in the [tex]\(35\%\)[/tex] solution is:
[tex]\[ 0.35 v \text{ gallons of acetic acid} \][/tex]
- The total volume of the mixture:
[tex]\[ v + 0.5 \text{ gallons} \][/tex]
- The amount of acetic acid in the mixture:
[tex]\[ 0.15 (v + 0.5) \text{ gallons of acetic acid} \][/tex]
Given that we want the total amount of acetic acid in the mixture to be the sum of the amount from the [tex]\(10\%\)[/tex] and [tex]\(35\%\)[/tex] solutions, we can set up the equation:
[tex]\[ 0.05 + 0.35 v = 0.15 (v + 0.5) \][/tex]
From the values calculated:
[tex]\[ v = 0.125 \text{ gallons} \][/tex]
Now, let's fill out the required table with these values:
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{c}
Amount of \\
Solution
\end{tabular} & \begin{tabular}{c}
Acid \\
Concentration
\end{tabular} & \begin{tabular}{c}
Amount of \\
Acid
\end{tabular} \\
\hline
[tex]$10\%$[/tex] Acid & [tex]$0.5$[/tex] gal & [tex]$0.10$[/tex] & [tex]$(0.10)(0.5) = 0.05$[/tex] \\
\hline
[tex]$35\%$[/tex] Acid & [tex]$v = 0.125$[/tex] gal & [tex]$0.35$[/tex] & [tex]$0.35 (0.125) = 0.04375$[/tex] \\
\hline
Mixture & [tex]$v + 0.5 = 0.625$[/tex] gal & [tex]$0.15$[/tex] & [tex]$0.15 (0.625) = 0.09375$[/tex] \\
\hline
\end{tabular}
So, the filled table is:
> \begin{tabular}{|c|c|c|c|}
> \hline & \begin{tabular}{c}
> Amount of \\
> Solution
> \end{tabular} & \begin{tabular}{c}
> Acid \\
> Concentration
> \end{tabular} & \begin{tabular}{c}
> Amount of \\
> Acid
> \end{tabular} \\
> \hline [tex]$10\%$[/tex] Acid & [tex]$0.5$[/tex] gal & [tex]$0.10$[/tex] & [tex]$0.05$[/tex] \\
> \hline [tex]$35\%$[/tex] Acid & [tex]$0.125$[/tex] gal & [tex]$0.35$[/tex] & [tex]$0.04375$[/tex] \\
> \hline Mixture & [tex]$0.625$[/tex] gal & [tex]$0.15$[/tex] & [tex]$0.09375$[/tex] \\
> \hline
> \end{tabular}
This table now accurately represents the given problem and the quantities involved.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.
