Question

B. The average of four consecutive odd
numbers is 24. Find the largest number.​

Answer 1

⇒ Given:

The average of four consecutive odd numbers is 24.

⇒ To Find:

The largest number.

⇒ Analysis:

In this question, we first have to provide an algebraic expression for each odd number. The first number would be a single variable and the rest would be the sum of the variable with an even number each. Putting the values in the equation of a mean, we will be able to find the answer.

⇒ Formula to be used:

→ $\boxed{\sf{Mean=\dfrac{Sum\:of\:all\:the\:values}{No.\:of\:values}}}$

⇒ Solution:

Let the first odd number be x.

The other three odd numbers are:

x + 2, x + 4 , x + 6

The number of odd numbers is 4.

We know that the mean of the numbers is 24.

Forming an equation:

$\sf{24\dfrac{x+x+2+x+4+x+6}{4}}$

$\sf{24=\dfrac{4x+12}{4}}$

$\sf{24\times4=4x+12}$

$\sf{96=4x+12}$

$\sf{96-12=4x}$

$\sf{84=4x}$

$\sf{x=\dfrac{84}{4}}$

$\sf{x=21}$

Hence the value of x is 21.

The greatest number in this set is x + 6.

x + 6 = 21 + 6

= 27

Hence the greatest odd number is 27.