The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 yea

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The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?

Mean is another word for average.

Mean age of women = Sum of all ages women / number of women

We're told mean age of women is 30, so we have:
Sum of all ages women / 10 = 30

Cross multiply, and we get:
Sum of all ages of women = 30 * 10
Sum of all ages of women = 300

Mean age of men = Sum of all ages men / number of men

We're told mean age of men is 29, so we have:
Sum of all ages men / 10 = 29

Cross multiply, and we get:
Sum of all ages of men = 29 * 10
Sum of all ages of men = 290

Calculate mean age (nearest year) of all the people in the office:
mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office
mean age of all the people in the office = (300 + 290) / (10 + 10)
mean age of all the people in the office = 590 / 20
mean age of all the people in the office = 29.5

The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30.
Because the decimal is greater or equal to 0.5 (halfway), we round up to 30