The total weight of 27 boxes of sweets is `20 (1)/(4)` kg. If each box weighs the same, find the weight of each box.

Answer

To find the weight of each box when the total weight of 27 boxes of sweets is \(20 \frac{1}{4}\) kg, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The total weight is given as \(20 \frac{1}{4}\) kg. To convert this to an improper fraction:
- Multiply the whole number (20) by the denominator (4):
\[ 20 \times 4 = 80 \]
- Add the numerator (1) to this result:
\[ 80 + 1 = 81 \]
- Therefore, \(20 \frac{1}{4}\) can be written as:
\[ \frac{81}{4} \text{ kg} \]

### Step 2: Divide the total weight by the number of boxes
Now, we need to find the weight of each box by dividing the total weight by the number of boxes (27):
\[ \text{Weight of each box} = \frac{81}{4} \div 27 \]

### Step 3: Change the division to multiplication
To divide by a number, we can multiply by its reciprocal. The reciprocal of 27 is \(\frac{1}{27}\):
\[ \frac{81}{4} \div 27 = \frac{81}{4} \times \frac{1}{27} \]

### Step 4: Simplify the multiplication
Now, we can multiply the fractions:
\[ \frac{81 \times 1}{4 \times 27} = \frac{81}{108} \]

### Step 5: Simplify the fraction
Next, we simplify \(\frac{81}{108}\):
- Both 81 and 108 can be divided by 27:
\[ 81 \div 27 = 3 \quad \text{and} \quad 108 \div 27 = 4 \]
- Thus, we have:
\[ \frac{81}{108} = \frac{3}{4} \]

### Step 6: Write the final answer
The weight of each box is:
\[ \frac{3}{4} \text{ kg} \]

### Final Answer
The weight of each box is \(\frac{3}{4}\) kg.

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