Question

the average of 5 numbers is 306, the average of first two number is 431 and the average of last two number is 214.5, what is tha third number?​

Answer 1

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Answer 2

1) Let the numbers be p, q, r, s, t

Average of 5 numbers = 306

Sum of observations/Sum of observations = 306

(p + q + r + s + t)/5 = 306

p + q + r + s + t = 306 * 5

p + q + r + s + t = 1530 --- eq (1)

2) Average of first two numbers = 431

Sum of observations/Number of observations = 431

(p + q)/2  = 431

p + q = 431 * 2

p + q = 862 ----- eq(2)

3) Average of last two numbers = 214.5

Sum of observations/Number of observations = 214.5

(s + t)/2  = 214.5

s+ t  = 214.5 * 2

s + t  = 429 ---- eq(3)

4) Substitute eq(3) and (2) in eq(1) to know the value of third number

p + q + r + s + t = 1530

(p + q) + r + (s + t) = 1530

862 + r + 429 = 1530

r + 1291 = 1530

r = 1530 - 1291

r = 239

Therefore the third number is 239.