Question

The average of five events is 40. The average of the first 2 events is 70 and the average of next two events is 65. Find the third number.

Answer 1

Answer:

The third number = -70

Step-by-step explanation:

Given,

The average of five events = 40

The average of the first 2 events  = 70

The average of the next two events  = 65

To find,

The third number

Recall the formula

Average = $\frac{sum \ of \ events }{total \ number \ of \ events}$

Solution:

Let $a_1, a_2,a_3,a_4,a_5$ be the five events

The average of these five events =  $\frac{a_1+a_2+a_3+a_4+a_5 }{5}$ =40

Then, $a_1 + a_2 + a_3 + a_4 + a_5 = 200$ --------------(1)

Given, that the average of two events is 70

Let $a_1 , a_2$  be those two events

$\frac{a_1+a_2 }{2}$ = 70

$a_1 + a_2$ = 140 ----------(2)

The average of the next two events is 65.

Let $a_3, a_4$ be those two events.

Then, $\frac{a_3 + a_4}{2}$ = 65

$a_3 +a_4$ = 65 ×2 = 130

$a_3 +a_4$ = 130 ---------------(3)

Substituting these values in equation(1)

140 +130 + $a_5$  = 200

270 + $a_5$ = 200

$a_5 = - 70$

∴ The third number = -70

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