Certainly! Let's walk through the solution step-by-step.
### Problem
We need to share a total amount of 90 based on a given ratio. Let's suppose the ratio is [1, 2, 3].
### Step-by-Step Solution
1. Understand the Ratio:
The ratio 1:2:3 means that for every 1 part given to the first person, the second person gets 2 parts, and the third person gets 3 parts.
2. Sum of Parts in the Ratio:
First, we need to find the total sum of the parts in the ratio:
[tex]\[
1 + 2 + 3 = 6
\][/tex]
3. Calculate Each Share:
Next, we determine how much each part is worth by dividing the total amount (90) by the sum of the parts (6).
[tex]\[
\text{Value per part} = \frac{90}{6} = 15
\][/tex]
4. Distribute According to the Ratio:
Now, we can calculate the individual shares:
- First part: [tex]\(1 \times 15 = 15\)[/tex]
- Second part: [tex]\(2 \times 15 = 30\)[/tex]
- Third part: [tex]\(3 \times 15 = 45\)[/tex]
### Final Result
Therefore, the total amount of 90 is distributed as follows based on the ratio 1:2:3:
- The first person receives 15.
- The second person receives 30.
- The third person receives 45.
This distribution ensures that the ratio 1:2:3 is maintained and the total amount adds up to 90. The total sum of the shares is [tex]\(15 + 30 + 45 = 90\)[/tex].
