# Question #8d811

Jul 1, 2016

The right answer is (b) $69$

#### Explanation:

Let the height of five men be ${H}_{1}$, ${H}_{2}$, ${H}_{3}$, ${H}_{4}$ and ${H}_{5}$.

We know that

(1) $\frac{{H}_{1} + {H}_{2} + {H}_{3} + {H}_{4} + {H}_{5}}{5} = 68$

(2) ${H}_{1} = 70$

(3) $\frac{{H}_{2} + {H}_{3} + {H}_{4}}{3} = 67$

Our task is to determine ${H}_{5}$

SOLUTION

From (1):
(4) ${H}_{1} + {H}_{2} + {H}_{3} + {H}_{4} + {H}_{5} = 5 \cdot 68 = 340$

From (3):
(5) ${H}_{2} + {H}_{3} + {H}_{4} = 3 \cdot 67 = 201$

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:
$\frac{{H}_{1} + {H}_{2} + {H}_{3} + {H}_{4} + {H}_{5}}{5} = \frac{70 + 201 + 69}{5} = \frac{340}{5} = 68$