Get the answers you need from a community of experts on IDNLearn.com. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.
Sagot :
Let's solve the problem step by step, filling in the values into the table as we go.
1. Amount of juice in the original solution:
- The original solution is 10 gallons and it contains 15% juice.
- Amount of juice in the original solution is calculated as:
[tex]\[ a = 10 \times \frac{15}{100} = 1.5 \text{ gallons} \][/tex]
2. Original amount of solution in gallons:
- Given that the original solution is 10 gallons.
[tex]\[ b = 10 \text{ gallons} \][/tex]
3. Amount of juice added:
- No additional juice is added, we are only adding pure water.
[tex]\[ c = 0 \text{ gallons} \][/tex]
4. Total solution added:
- Let's denote the amount of pure water added as [tex]\( d \)[/tex].
- We can use the resulting percentage to find [tex]\( d \)[/tex].
- The new solution should have a 5\% juice concentration.
- The amount of juice in the final solution will be the same as the amount of juice in the original solution since we are adding only water.
- To find [tex]\( d \)[/tex], we use the relationship that the final concentration should be 5% when the juice amount remains 1.5 gallons.
- Let [tex]\( x \)[/tex] be the amount of pure water added.
- The new total amount of solution is [tex]\( 10 + x \)[/tex] gallons.
- The concentration equation is:
[tex]\[ \frac{1.5}{10 + x} \times 100 = 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ 1.5 = 0.05 \times (10 + x) \][/tex]
[tex]\[ 1.5 = 0.5 + 0.05x \][/tex]
[tex]\[ 1 = 0.05x \][/tex]
[tex]\[ x = 20 \][/tex]
- Therefore, the amount of pure water added is:
[tex]\[ d = 20 \text{ gallons} \][/tex]
Using the above calculations, we can now fill in the table:
| | Original | Added | New |
|---------------------------|----------|-------|-------------------|
| Amount of juice | [tex]\( a = 1.5 \)[/tex] | [tex]\( c = 0 \)[/tex] | [tex]\( 1.5 \)[/tex] |
| Total solution | [tex]\( b = 10 \)[/tex] | [tex]\( d = 20 \)[/tex] | [tex]\( 30 \)[/tex] |
So, the gallons of pure water to be added to the solution are 20 gallons.
1. Amount of juice in the original solution:
- The original solution is 10 gallons and it contains 15% juice.
- Amount of juice in the original solution is calculated as:
[tex]\[ a = 10 \times \frac{15}{100} = 1.5 \text{ gallons} \][/tex]
2. Original amount of solution in gallons:
- Given that the original solution is 10 gallons.
[tex]\[ b = 10 \text{ gallons} \][/tex]
3. Amount of juice added:
- No additional juice is added, we are only adding pure water.
[tex]\[ c = 0 \text{ gallons} \][/tex]
4. Total solution added:
- Let's denote the amount of pure water added as [tex]\( d \)[/tex].
- We can use the resulting percentage to find [tex]\( d \)[/tex].
- The new solution should have a 5\% juice concentration.
- The amount of juice in the final solution will be the same as the amount of juice in the original solution since we are adding only water.
- To find [tex]\( d \)[/tex], we use the relationship that the final concentration should be 5% when the juice amount remains 1.5 gallons.
- Let [tex]\( x \)[/tex] be the amount of pure water added.
- The new total amount of solution is [tex]\( 10 + x \)[/tex] gallons.
- The concentration equation is:
[tex]\[ \frac{1.5}{10 + x} \times 100 = 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ 1.5 = 0.05 \times (10 + x) \][/tex]
[tex]\[ 1.5 = 0.5 + 0.05x \][/tex]
[tex]\[ 1 = 0.05x \][/tex]
[tex]\[ x = 20 \][/tex]
- Therefore, the amount of pure water added is:
[tex]\[ d = 20 \text{ gallons} \][/tex]
Using the above calculations, we can now fill in the table:
| | Original | Added | New |
|---------------------------|----------|-------|-------------------|
| Amount of juice | [tex]\( a = 1.5 \)[/tex] | [tex]\( c = 0 \)[/tex] | [tex]\( 1.5 \)[/tex] |
| Total solution | [tex]\( b = 10 \)[/tex] | [tex]\( d = 20 \)[/tex] | [tex]\( 30 \)[/tex] |
So, the gallons of pure water to be added to the solution are 20 gallons.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.
