Question 632031: The average weight of 3 men A,B and C is 85kg. Another man D joins the group the average weight becomes 81kg. If another man E whose weight is 4kg more than that of D,replace A the average weight of B,C,D and E becomes 78kg. What is the weight of A?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a is equal to 85 kg.
here's how it works.
(a+b+c)/3 = 85
this means that a+b+c = 3*85 = 255
d joins the group and the average weight is now 81 kg.
this means that (a+b+c+d)/4 = 81 which means that a+b+c+d = 4*81 = 324
this means that d has to weight 324 - 255 = 69 kg.
since e weighs 4 kg more than d, this means that e weighs 73 kg.
when e replaces a, the average weight becomes 78 kg.
this means the (b+c+d+e)/4 = 78
this means that b+c+d+e = 78*4 = 312 kg.
we have:
a+b+c+d = 324 kg
b+c+d+e = 312 kg
the difference is 12 kg.
the difference from the first equation to the second equation is equal to -12.
this means that the second equation is 12 kg less than the first equation.
in order to get there, we subtracted a and added e.
this means that e-a = -12
we know that e is equal to 73 kg, so the equation becomes:
73-a = -12
if we add a to both sides of this equation and add 12 to both sides of this equation we get:
73+12 = a
combine like terms to get 85 = a
commute this result to get:
a = 85 kg.
we started off with a+b+c = 3*85
since a is equal to 85, this equation becomes:
85+b+c = 3*85 = 255
we added d to get:
85+b+c+d = 4*81 = 324
we found out that d was equal to 324-255 = 69 kg
we found out that e was equal to 69+4 = 73 kg
with d equal to 69 kg, our equation became:
85+b+c+69 = 324
we got rid of a and added e so our equation became:
b+c+69+73 = 312
what happened was we lost 85 kg and gained 73 kg.
324 - 85 + 73 = 312
the fact that a is equal to 85 kg makes this correct.
the key to solving this problem is that the average times the number of elements is equal to the total.
(a+b+c)/3 = 85 which is the average
the average of 85 * 3 = 255 which is the total.
that concept makes the problem doable.
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