Let's solve the given problem step-by-step, filling in the missing parts of the table and explaining how we arrive at the results.
1. Original Amount of Broth:
- The original pot of soup is 50 liters, and it is 50% broth.
- Compute the original amount of broth:
[tex]\[
50\% \text{ of } 50 \text{ liters} = 0.50 \times 50 = 25 \text{ liters}
\][/tex]
2. Original Total Solution:
- The original total solution is 50 liters (given).
3. Added Amount:
- We only add pure water, which contains 0 liters of broth.
4. New Total Solution:
- Adding 10 liters of pure water to the original 50 liters:
[tex]\[
50 \text{ liters} + 10 \text{ liters} = 60 \text{ liters}
\][/tex]
5. New Amount of Broth:
- The amount of broth remains unchanged since we only added water (i.e., 25 liters).
6. New Percentage of Broth:
- To find out the new percentage of broth in the solution, we set up the ratio of broth to the total solution:
[tex]\[
\frac{25}{60} = \frac{x}{100}
\][/tex]
- Solving for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{25}{60} \times 100 = 41.6667\%
\][/tex]
Now, we fill in the table:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline & \text{Original} & \text{Added} & \text{New} \\
\hline
\text{Amount of broth} & 25 & 0 & 25\\
\hline
\text{Total solution} & 50 & 10 & 60\\
\hline
\end{array}
\][/tex]
Therefore, we get:
1. [tex]\(c = 25\)[/tex]
2. [tex]\(d = 60\)[/tex]
Finally, the equation relating the new ratio of broth to the new total solution to the new percentage of broth is:
[tex]\[
\frac{25}{60} = \frac{x}{100}
\][/tex]
