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The container that holds the water for the football team is [tex]\(\frac{1}{5}\)[/tex] full. After pouring in 14 gallons of water, it is [tex]\(\frac{7}{10}\)[/tex] full. How many gallons can the container hold?

[tex]\(\square\)[/tex] gallons



Answer :

GinnyAnswer
To determine the total capacity of the container, let's go through the given information step by step.

1. Initial Information:
- The container is initially [tex]\( \frac{1}{5} \)[/tex] full.
- After pouring in 14 gallons of water, the container is [tex]\( \frac{7}{10} \)[/tex] full.

2. Identify the change in the container's fullness:
- Initial proportion: [tex]\( \frac{1}{5} = 0.2 \)[/tex]
- Final proportion: [tex]\( \frac{7}{10} = 0.7 \)[/tex]

The change in the proportion of the container's capacity (fullness) is:
[tex]\[ 0.7 - 0.2 = 0.5 \][/tex]

3. Relate the change in fullness to the added volume:
- The change in the proportion of the container's capacity is 0.5.
- This change corresponds to the 14 gallons of water that were poured in.

4. Calculate the total capacity of the container:
- If 0.5 of the container’s capacity equals 14 gallons, we can set up the proportion to find the total capacity [tex]\( C \)[/tex]:
[tex]\[ 0.5C = 14 \][/tex]
- Solving for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{14}{0.5} = 28 \][/tex]

Therefore, the total capacity of the container is:
[tex]\[ \boxed{28} \][/tex]
gallons.

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