The weights of two bags are in the ratio `7:6.` If the total weight of both bags in 91 kg, find the weight of each bag.

Answer

To solve the problem step by step, we will follow the method of ratios and proportions.

### Step 1: Understand the ratio
The weights of the two bags are given in the ratio of 7:6. This means that for every 7 parts of weight in Bag 1, Bag 2 has 6 parts of weight.

### Step 2: Calculate the total parts in the ratio
To find the total parts represented by the ratio, we add the parts of both bags:
\[ 7 + 6 = 13 \]
So, the total parts in the ratio is 13.

### Step 3: Set up the equation for the total weight
We know that the total weight of both bags is 91 kg. We can express this in terms of the parts from the ratio:
\[ \text{Total weight} = \text{Total parts} \times \text{Weight per part} \]
Let the weight per part be \( x \). Therefore, we can write:
\[ 13x = 91 \]

### Step 4: Solve for the weight per part
To find the value of \( x \), we divide both sides of the equation by 13:
\[ x = \frac{91}{13} \]
Calculating this gives:
\[ x = 7 \text{ kg} \]

### Step 5: Calculate the weight of each bag
Now that we have the weight per part, we can find the weight of each bag:
- For Bag 1 (7 parts):
\[ \text{Weight of Bag 1} = 7 \times x = 7 \times 7 = 49 \text{ kg} \]
- For Bag 2 (6 parts):
\[ \text{Weight of Bag 2} = 6 \times x = 6 \times 7 = 42 \text{ kg} \]

### Final Answer
- Weight of Bag 1 = 49 kg
- Weight of Bag 2 = 42 kg