The average age of 8 men is increased by 2 when one of them, whose age is twenty years, is replaced by a new man.What is the age of the new man?

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Answer 1 · 2018-04-24T04:22:58

#36#

.

If #x_1# through #x_8# are the ages of the initial #8# men and the average of them is #y# then we can write:

#(x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8)/8=y#

Now, we replace #x_8# with #20#:

#(x_1+x_2+x_3+x_4+x_5+x_6+x_7+20)/8=y# #color(red)(Equation-1)#

Let's call the new man's age #z#:

#(x_1+x_2+x_3+x_4+x_5+x_6+x_7+z)/8=y+2# #color(red)(Equation-2)#

Let's subtract #color(red)(Equation-1)# from #color(red)(Equation-2)#:

#y+2-y=(x_1+x_2+x_3+x_4+x_5+x_6+x_7+z)/8-(x_1+x_2+x_3+x_4+x_5+x_6+x_7+20)/8#

#2=z/8-20/8#

#2=(z-20)/8#

#z-20=16#

#z=36#

Answer 2 · 2018-04-24T06:29:22

The new man is #36# years old.

#Mean = "total"/"number of men"#

Let the average age of each man be #x# years

Total age for the #8# men = #8xx x = 8x#

One man (age #20#) is removed so the Total decreases:

#"Total" = 8x-20#

He is replaced by another man of age #m#.

#"Total" = 8x-20+m#

This increases the average age by #2# so the new total will be #16# more.

Write an equation to indicate this:

#8x -20+m = 8(x+2)#

#cancel(8x) -20+m = cancel(8x)+16#

#m =16+20#

#m=36#

The new man is #36# years old.