Question

There are seven consecutive even numbers.
If the largest number is x, write an algebraic
expression for the middle number. If the
middle number is 48, find the value of the
smallest number.​

Answer 1

ANSWER:

The smallest number = 42

Algebraic expression for the middle number = ( x - 6 )

GIVEN:

The largest consecutive even number is x

Middle number = 48

TO FIND:

Algebraic expression for the middle number and the value of the smallest number.

EXPLANATION:

$7^{th}$ number = x

As the numbers are even , the number before x must be (x - 2 )

$6^{th}$ number = x - 2

Proceed in a similar way for the other terms also. We will get,

$5^{th}$ number = x - 4

$4^{th}$ number = x - 6

$3^{rd}$ number = x - 8

$2^{nd}$ number = x - 10

$1^{st}$ number = x - 12

$4^{th}$ is the middle term and its expression is ( x - 6 )

Also x - 6 = 48 => x = 54

The largest number = 54

The smallest number = x - 12 => 54 - 12 = 42