Certainly! Let's go through the solution step-by-step based on the information given in the question.
1. Understanding the initial setup:
- We start with a 50-liter pot of soup.
- This soup is 50% broth, meaning 50% of the 50 liters is broth.
- Amount of broth in the initial 50 liters [tex]\( = 50\% \times 50 \)[/tex] = 25 liters of broth.
2. Adding pure water:
- We add 10 liters of pure water to the soup.
3. New Total Solution:
- The total amount of the solution after adding water = original amount + added water
- New total amount [tex]\( = 50 \, \text{liters} + 10 \, \text{liters} = 60 \, \text{liters} \)[/tex]
4. Amount of Broth in the New Solution:
- Since we only added pure water (which contains no broth), the amount of broth remains the same as before.
- The amount of broth in the new solution remains [tex]\( 25 \)[/tex] liters.
Given this information, we can fill in the missing parts of the table as follows:
[tex]\[
\begin{array}{l}
c=\square \\
d=\checkmark
\end{array}
\][/tex]
[tex]\[
\begin{array}{|l|c|c|c|}
\hline
& \text{Original} & \text{Added} & \text{New} \\
\hline
\begin{array}{l}
\text{Amount of} \\
\text{broth}
\end{array}
& 25
& 0
& 25 \\
\hline
\begin{array}{l}
\text{Total} \\
\text{solution}
\end{array}
& 50
& 10
& 60 \\
\hline
\end{array}
\][/tex]
So, the final values are:
- [tex]\( c = 25 \)[/tex] liters (amount of broth in the new solution)
- [tex]\( d = 60 \)[/tex] liters (total amount of the new solution)
Therefore:
[tex]\[ c = 25 \][/tex]
[tex]\[ d = 60 \][/tex]
