If the weight of 18 sheets of paper is 50 g, how many sheets of the same paper will weight `3(3)/(4)`kg?

Options

A. 1386
B. 1836
C. 1350
D. 1314

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Convert the weight from kg to grams
We are given that the weight we need to find is \(3 \frac{3}{4}\) kg. First, we convert this to grams.

\[ 3 \frac{3}{4} \text{ kg} = 3.75 \text{ kg} \]

Since \(1 \text{ kg} = 1000 \text{ grams}\), we multiply:

\[ 3.75 \text{ kg} \times 1000 \text{ g/kg} = 3750 \text{ grams} \]

### Step 2: Determine the weight of one sheet of paper
We know that 18 sheets of paper weigh 50 grams. To find the weight of one sheet, we divide the total weight by the number of sheets:

\[ \text{Weight of one sheet} = \frac{50 \text{ grams}}{18 \text{ sheets}} \approx 2.78 \text{ grams/sheet} \]

### Step 3: Calculate how many sheets weigh 3750 grams
Now, we need to find out how many sheets weigh 3750 grams. We can do this by dividing the total weight we want by the weight of one sheet:

\[ \text{Number of sheets} = \frac{3750 \text{ grams}}{\text{Weight of one sheet}} = \frac{3750 \text{ grams}}{\frac{50 \text{ grams}}{18 \text{ sheets}}} \]

To simplify this calculation, we can multiply by the reciprocal:

\[ \text{Number of sheets} = 3750 \text{ grams} \times \frac{18 \text{ sheets}}{50 \text{ grams}} = \frac{3750 \times 18}{50} \]

### Step 4: Simplify the calculation
Now we can simplify:

1. First, calculate \(3750 \div 50 = 75\).
2. Then, multiply by 18:

\[ 75 \times 18 = 1350 \]

### Conclusion
Thus, the number of sheets that will weigh \(3 \frac{3}{4}\) kg is **1350 sheets**.

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