Question

One quarter of the sum of two consecutive odd numbers is 14.Find the odd numbers

Answer 1

n and n + 2
(1/4) (2 n+2) = 14
2 n + 2 = 56
2 n = 54
n = 27
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check
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(27+29) /4
56/4
14 sure enough

Answer 2

Odd numbers have the general form:

n = 2 k - 1

where

k = real number (1, 2, 3...)

The first number is:

n1 = 2 k - 1

The difference between two consecutive odd numbers is 2, so the second number is:

n2 = n1 + 2 = 2 k - 1 + 2 = 2 k + 1

One quarter of the sum of two consecutive odd numbers is 14 means:

1 / 4 ( n1 + n2 ) = 14

Multiply both sides by 4.

n1 + n2 = 56

2 k - 1 + 2 k + 1 = 56

4 k = 56

k = 56 / 4

k = 14

The first odd number is:

n1 = 2 k - 1

n1 = 2 • 14 - 1 = 28 - 1 = 27

The second odd number is:

n2 = 2 k + 1

n2 = 2 • 14 + 1 = 28 + 1 = 29

So two consecutive odd numbers are 27 and 29.

Check the result.

( 27 + 29 ) / 4 = 56 / 4 = 14