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 reasoning provided in the video transcript.

### Step 1: Determine the weight of one sheet of paper
We know that the weight of 18 sheets of paper is 50 grams. To find the weight of one sheet, we divide the total weight by the number of sheets:

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

### Step 2: Convert the given weight from kg to grams
The problem states that we need to find out how many sheets weigh \(3 \frac{3}{4}\) kg. First, we convert this mixed number into an improper fraction:

\[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \text{ kg} \]

Next, we convert kilograms to grams (since 1 kg = 1000 grams):

\[ \text{Total weight in grams} = \frac{15}{4} \text{ kg} \times 1000 \text{ grams/kg} = \frac{15 \times 1000}{4} = \frac{15000}{4} = 3750 \text{ grams} \]

### Step 3: Calculate the number of sheets
Now, we need to find out how many sheets correspond to 3750 grams. We will divide the total weight by the weight of one sheet:

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

To divide by a fraction, we multiply by its reciprocal:

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

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

\[ = \frac{3750 \times 18}{50} \]

First, simplify \(3750 \div 50\):

\[ 3750 \div 50 = 75 \]

Now, multiply by 18:

\[ 75 \times 18 = 1350 \]

### Final Answer
Thus, the number of sheets of paper that will weigh \(3 \frac{3}{4}\) kg is:

\[ \boxed{1350} \]

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