My question is related to math averages.

Question

The average weight of 8 men is increased by 1.5kg when one of the men who weights 65kg is replaced by a new man. Find the weight of the new man.

Please share with me the complete solution with description. Thank you.

Answer 1

since the average increases, the new man must weight more than 65 lbs.

Let S be the sum of the first 7 men.

The average A = (S + 65)/8

8A = S + 65

Upon replacement:

8(A+1.5) = S + 65 + x where x is the difference in the weights

8A + 1.5*8 = S + 65 + x

8A + 12 = S + 65 + x

S + 65 + 12 = S + 65 + x

x = 12

The new man weights 12 pounds more or 65+12 = 77 lbs.