Certainly! Let's solve the problem of sharing an amount of 240 in the ratio 5:7 step by step.
### Step 1: Understand the Ratio
The ratio 5:7 means that for every 5 parts given to the first share, 7 parts are given to the second share.
### Step 2: Find the Total Number of Parts
First, you need to find the total number of parts by adding the two parts of the ratio together:
[tex]\[ 5 + 7 = 12 \][/tex]
### Step 3: Calculate the Value of One Part
Next, divide the total amount (240) by the total number of parts (12) to find the value of one part:
[tex]\[ \text{Value per part} = \frac{240}{12} = 20 \][/tex]
### Step 4: Calculate Each Share
Using the value of one part, you can now find each share:
#### First Share:
Multiply the value of one part (20) by the number of parts for the first share (5):
[tex]\[ \text{First Share} = 5 \times 20 = 100 \][/tex]
#### Second Share:
Multiply the value of one part (20) by the number of parts for the second share (7):
[tex]\[ \text{Second Share} = 7 \times 20 = 140 \][/tex]
### Final Answer:
- The first share is 100.
- The second share is 140.
Therefore, the amount of 240 is shared in the ratio 5:7 as 100 and 140.
### Summary:
- Total parts: 12
- Value per part: 20
- First share: 100
- Second share: 140
