You and Bruce Willis are upright in a natatorium of liquid with containers of 5.3 gallons and 3.75. You need exactly 4 1/2 gallons of liquid to create a certain solution. How can you assure that you have exactly that amount? Show your work.
To ensure you have exactly 4 1/2 gallons of liquid, you can follow these steps:
1. Start by using the 5.3-gallon container:
- Fill the 5.3-gallon container completely.
2. Transfer the liquid from the 5.3-gallon container to the 3.75-gallon container:
- Pour the liquid from the 5.3-gallon container into the 3.75-gallon container.
- The 3.75-gallon container will be completely filled, leaving 1.55 gallons (5.3 - 3.75) in the 5.3-gallon container.
3. Empty the 3.75-gallon container:
- Pour out all the liquid from the 3.75-gallon container, making it empty.
4. Transfer the remaining liquid from the 5.3-gallon container to the 3.75-gallon container:
- Pour the remaining 1.55 gallons from the 5.3-gallon container into the 3.75-gallon container.
- The 3.75-gallon container will now have 1.55 gallons of liquid.
5. Use the 5.3-gallon container again:
- Fill the 5.3-gallon container completely.
6. Transfer as much liquid as possible from the 5.3-gallon container to the 3.75-gallon container:
- Pour the liquid from the 5.3-gallon container into the 3.75-gallon container until the 3.75-gallon container is full.
- You will be left with 2.8 gallons (5.3 - 2.5) in the 5.3-gallon container.
7. Combine the contents of the 3.75-gallon and 5.3-gallon containers:
- Pour the liquid from the filled 3.75-gallon container into the 5.3-gallon container that has 2.8 gallons.
- The total liquid in the 5.3-gallon container will be 2.8 + 3.75 = 6.55 gallons.
By following these steps, you will have surpassed the 4 1/2 gallons requirement and end up with 6.55 gallons of liquid.