The weight of an empty gas cylinder is `16(4)/(5) "kg"` and it contains `14(2)/(3) "kg"` of gas. What is the weight of the cylinder filled with gas?

Answer

To find the weight of the gas cylinder filled with gas, we need to add the weight of the empty gas cylinder and the weight of the gas it contains. Let's break this down step by step.

### Step 1: Convert the mixed numbers to improper fractions
1. The weight of the empty gas cylinder is given as \( 16 \frac{4}{5} \) kg.
- To convert this to an improper fraction:
\[ 16 \frac{4}{5} = \frac{(16 \times 5) + 4}{5} = \frac{80 + 4}{5} = \frac{84}{5} \text{ kg} \]

2. The weight of the gas is given as \( 14 \frac{2}{3} \) kg.
- To convert this to an improper fraction:
\[ 14 \frac{2}{3} = \frac{(14 \times 3) + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3} \text{ kg} \]

### Step 2: Add the two fractions
Now we need to add \( \frac{84}{5} \) kg and \( \frac{44}{3} \) kg. To do this, we first need a common denominator.

1. The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.

2. Convert both fractions to have the common denominator of 15:
- For \( \frac{84}{5} \):
\[ \frac{84}{5} = \frac{84 \times 3}{5 \times 3} = \frac{252}{15} \]
- For \( \frac{44}{3} \):
\[ \frac{44}{3} = \frac{44 \times 5}{3 \times 5} = \frac{220}{15} \]

3. Now add the two fractions:
\[ \frac{252}{15} + \frac{220}{15} = \frac{252 + 220}{15} = \frac{472}{15} \text{ kg} \]

### Step 3: Convert the improper fraction to a mixed number
To convert \( \frac{472}{15} \) kg to a mixed number:
1. Divide 472 by 15:
- \( 472 \div 15 = 31 \) (whole number part)
- Remainder: \( 472 - (31 \times 15) = 472 - 465 = 7 \)

2. So, \( \frac{472}{15} \) can be expressed as:
\[ 31 \frac{7}{15} \text{ kg} \]

### Final Answer
The total weight of the gas cylinder filled with gas is \( 31 \frac{7}{15} \) kg.

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