The average height of five men is 68 inches. If one man is 70 inches tall and three others have an average of 67 inches, the height of the fifth man, in inches, is? a) 68 b)69 c) 70 d) 71

The right answer is (b) ##69##

Let the height of five men be ##H_1##, ##H_2##, ##H_3##, ##H_4## and ##H_5##.

We know that

(1) ##(H_1+H_2+H_3+H_4+H_5)/5 = 68##

(2) ##H_1 = 70##

(3) ##(H_2+H_3+H_4)/3 = 67##

Our task is to determine ##H_5##

SOLUTION

From (1): (4) ##H_1+H_2+H_3+H_4+H_5 = 5 * 68 = 340##

From (3): (5) ##H_2+H_3+H_4 = 3*67 = 201##

Substitute (2) and (5) into (4) getting ##70+201+H_5 = 340## from which follows ##H_5 = 340-70-201 = 69##

CHECK the average height of all five men: ##(H_1+H_2+H_3+H_4+H_5)/5 = (70+201+69)/5 = 340/5=68##