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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  1. math_celebrity

    math_celebrity Administrator Staff Member

    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
     

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