Exercise

1. The mean age of a combined group of men and women is 30 years. If the mean age of the group of men is 32 and the mean age of the group of women is 27, find out the percentage of men and women in the group.

To solve this problem, we need to determine the percentage of men and women in a group based on the given average ages.

### Problem Breakdown:
1. The mean age of the combined group is 30 years.
2. The mean age of the group of men is 32 years.
3. The mean age of the group of women is 27 years.

### Steps to Solve:

1. Define Variables:
- Let [tex]$ x $[/tex] be the percentage of the group that are men. Therefore, [tex]$ 1 - x $[/tex] will be the percentage of the group that are women.

2. Set Up the Equation for the Mean Age:
- The mean age of the entire group can be expressed as a weighted average of the men's and women's mean ages:

[tex]\[
30 = (32 \times x) + (27 \times (1 - x))
\][/tex]

3. Simplify the Equation:
- Expand the expression:
[tex]\[
30 = 32x + 27 - 27x
\][/tex]

- Combine like terms:
[tex]\[
30 = 5x + 27
\][/tex]

4. Solve for [tex]$ x $[/tex]:
- Subtract 27 from both sides:
[tex]\[
30 - 27 = 5x
\][/tex]
[tex]\[
3 = 5x
\][/tex]

- Divide by 5 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{3}{5}
\][/tex]
[tex]\[
x = 0.6
\][/tex]

5. Calculate Percentages:
- The percentage of men is [tex]$ 0.6 \times 100 = 60\%$[/tex].
- The percentage of women is [tex]$ (1 - 0.6) \times 100 = 40\%$[/tex].

### Conclusion:
The percentage of men in the group is 60%, and the percentage of women is 40%.

Exercise1. The mean age of a combined group of men and women is 30 years. If the mean age of the group of men is 32 and the mean age of the group of women is 27, find out the percentage of men and women in the group.

Answer :

Other Questions

Exercise

1. The mean age of a combined group of men and women is 30 years. If the mean age of the group of men is 32 and the mean age of the group of women is 27, find out the percentage of men and women in the group.