# The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

Discussion in 'Calculator Requests' started by math_celebrity, May 20, 2020.

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The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?

The mean formulas is denoted as:
Mean = Sum of Ages / Total People

We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5

Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140

One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People

With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6

But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a

So we have:
29 = (140 + a)/6

Cross multiply:
140 + a = 29 * 6
140 + a = 174

To solve for a, we type this equation into our search engine and we get:
a = 34