Question

find three consecutive odd numbers such that 5 times the middle number is greater than the sum of the first and the last numbers by 495

Answer 1

Your Answer:

The numbers are 163, 165 and 167

Given:-

• Three consecutive odd numbers.
• 5 times the middle number is greater than the sum of the first and the last numbers by 495.

To Find:-

• The consecutive numbers

Solution:-

Let the numbers be (n-2), n and (n+2).

The numbers are taken by the difference of 2 because the difference between two odd numbers is 2

ATQ,

$\tt 5(n) = (n-2) + (n+2) + 495$

So, solving the equations further

$\tt 5n= n \cancel{-2}+n\cancel{+2} + 495 \\\\ \tt \Rightarrow 5n = 2n + 495\\\\ \tt \Rightarrow 5n -2n = 495 \\\\ \tt \Rightarrow (5-3)n = 495 \\\\ \tt \Rightarrow 3n = 495 \\\\ \tt \Rightarrow n =\dfrac{495}{3} \\\\ \tt \Rightarrow n= 165$

So, We get n = 165

So, n - 2 = 165 - 2 =163

n + 2 = 165 + 2 = 167

Answer 2

Answer:

The three consecutive odd numbers are 163,165 and 167

Step-by-step explanation:

Let the first odd number be x

second odd number be x+2

third odd number be x+4

Now A/Q,

5(x+2)=(x)+(x+4)+495

5x+10=x+x+4+495

5x+10=2x+499

5x-2x=499-10

3x=489

x=163

the first odd number = 163

the second odd number = x+2

=163+2

=165

the third odd number=x+4

=163+4

=167

So,the numbers are 163, 165, and 167