To determine how much each of the three men will receive from a total of [tex]$32,000, which is to be divided in the ratio 4:3:1, we need to follow these steps:
1. Understand the problem and the given ratio:
The ratio 4:3:1 tells us the proportion of the total amount each man gets. This means that if we divide the total amount into parts based on this ratio, the first man gets 4 parts, the second man gets 3 parts, and the third man gets 1 part.
2. Sum of the ratio parts:
Add the parts of the ratio together to find the total number of parts.
\[
4 + 3 + 1 = 8
\]
So, the total ratio parts equal 8.
3. Calculate the value of one part:
To find out how much one part is worth, divide the total amount by the total number of parts.
\[
\text{Value of one part} = \frac{32000}{8} = 4000
\]
4. Determine each man’s share:
Now multiply the value of one part by the number of parts each man gets according to the ratio.
- First man:
\[
\text{Share of the first man} = 4 \times 4000 = 16000
\]
- Second man:
\[
\text{Share of the second man} = 3 \times 4000 = 12000
\]
- Third man:
\[
\text{Share of the third man} = 1 \times 4000 = 4000
\]
Therefore, the amounts each man receives are:
- The first man receives $[/tex]16,000,
- The second man receives [tex]$12,000,
- The third man receives $[/tex]4,000.
