Let's work through the solution step-by-step to find out how many gallons of pure water need to be added.
First, let's define the quantities in the problem:
1. The original solution is 10 gallons with a 15% juice concentration.
### Calculate the amount of juice in the original solution:
- The amount of juice in the original solution (a) is 15% of 10 gallons:
[tex]\[
a = 0.15 \times 10 = 1.5 \text{ gallons}
\][/tex]
### Determine the original amount of solution in gallons:
- The original amount of solution (b) is
[tex]\[
b = 10 \text{ gallons}
\][/tex]
### How much juice is added:
- Since we are adding pure water, no additional juice is included:
[tex]\[
c = 0 \text{ gallons}
\][/tex]
### How much total solution is added:
- Let’s find out the amount of pure water we need to add. From our calculations:
[tex]\[
d = 20 \text{ gallons}
\][/tex]
Now, let's fill in the table:
[tex]\[
\text{What is the amount of juice in the original solution? } a = 1.5
\][/tex]
[tex]\[
\text{What is the original amount of solution in gallons? } b = 10
\][/tex]
[tex]\[
\text{How much juice is added? } c = 0
\][/tex]
[tex]\[
\text{How much total solution is added? } d = 20
\][/tex]
Here is the filled table:
\begin{tabular}{|c|c|c|c|}
\hline
& Original & Added & New \\
\hline
Amount of juice & [tex]$1.5$[/tex] & [tex]$0$[/tex] & [tex]$1.5$[/tex] \\
\hline
Total solution & [tex]$10$[/tex] & [tex]$20$[/tex] & [tex]$30$[/tex] \\
\hline
\end{tabular}
So, the amount of pure water that should be added to achieve a 5% juice concentration in the solution is:
[tex]\[
d = 20 \text{ gallons}
\][/tex]
