Question 16 A tank of water was $$ \frac{3}{4} $$ full. Watering the animals used $$ \frac{3}{10} $$ of a full tank and another $$ \frac{1}{5} $$ of a full tank was used to water the vegetables. Rainfall increased the tank level back to $$ \frac{3}{8} $$ full. What fraction of the tank was filled by the rain?

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1. Initially, the tank was $$ \frac{3}{4} $$ full.

2. Watering the animals used $$ \frac{3}{10} $$ of a full tank, and watering the vegetables used $$ \frac{1}{5} $$ (which is equivalent to $$ \frac{2}{10} $$) of a full tank. The total used is:
   $$
   \frac{3}{10} + \frac{2}{10} = \frac{5}{10} = \frac{1}{2}
   $$

3. After watering, the tank was:
   $$
   \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}
   $$

4. Rainfall increased the water level to $$ \frac{3}{8} $$. Let $$ x $$ be the fraction of the tank filled by the rain. Then:
   $$
   \frac{1}{4} + x = \frac{3}{8}
   $$

5. To solve for $$ x $$, first express $$ \frac{1}{4} $$ as $$ \frac{2}{8} $$:
   $$
   \frac{2}{8} + x = \frac{3}{8}
   $$

6. Subtract $$ \frac{2}{8} $$ from both sides to isolate $$ x $$:
   $$
   x = \frac{3}{8} - \frac{2}{8} = \frac{1}{8}
   $$

$$
\boxed{\frac{1}{8}}
$$
The rain filled $$ \frac{1}{8} $$ of the tank.

Question 16
A tank of water was full. Watering the animals used of a full tank and another of a full tank was used to water the
vegetables. Rainfall increased the tank level back to full. What fraction of the tank was filled by the rain?

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Question 16 A tank of water was full. Watering the animals used of a full tank and another of a full tank was used to water the vegetables. Rainfall increased the tank level back to full. What fraction of the tank was filled by the rain?