To solve the problem of sharing 187 in the ratio [tex]\(5:4:2\)[/tex], let’s proceed step-by-step.
1. Understand the ratio:
- The ratio [tex]\(5:4:2\)[/tex] indicates that we need to divide the total amount into 3 parts such that the first part is 5 units, the second part is 4 units, and the third part is 2 units.
2. Sum up the parts of the ratio:
- Add up the parts of the ratio to find the total number of parts into which the amount is divided.
[tex]\[
5 + 4 + 2 = 11
\][/tex]
3. Calculate the value of one part:
- Divide the total amount (187) by the total number of parts (11) to find the value of one unit.
[tex]\[
\text{Value of one part} = \frac{187}{11} = 17
\][/tex]
4. Calculate each share:
- Multiply the value of one part by each part of the ratio to find the corresponding amounts.
- For the first share (5 parts):
[tex]\[
\text{First share} = 5 \times 17 = 85
\][/tex]
- For the second share (4 parts):
[tex]\[
\text{Second share} = 4 \times 17 = 68
\][/tex]
- For the third share (2 parts):
[tex]\[
\text{Third share} = 2 \times 17 = 34
\][/tex]
5. Conclusion:
- The original amount of 187 is shared in the ratio [tex]\(5:4:2\)[/tex] as follows:
[tex]\[
85, 68, 34
\][/tex]
Thus, the amounts corresponding to the ratio [tex]\(5:4:2\)[/tex] for a total of 187 are 85, 68, and 34 respectively.
