Question

the sum of three alternate numbers are 3 less than 24 .find the numbers
answer- is 5,7,9
need formula in linear equation​

Answer 1

Given :-

Sum of three alternate numbers are 3 less than 24.

To find :-

The numbers.

What are alternative numbers?

Consecutive even or odd numbers are said to be alternative.

Example : 2 and 4. 3 and 5.

Let's solve!

Let the first number be x.

As it's clearly given in the question that they are alternative numbers, the next number will be x+2 and the third one will be x+4.

According to the question,

(x + x+2 + x+4) ≤ 24

Hence by adding 3 to the LHS(Left Hand Side) or subtracting 3 from the RHS(Right Hand Side), an equation is formed.

Method 1 :

By adding 3 to the LHS,

x + x+2 + x+4 +3 = 24

adding all the variables and constants

3x + 9 = 24

Transposing 9 to the RHS, so all the variables are on one side and constants on the other,

3x = 24 - 9

3x =  15

Transposing 3 to the RHS,

Therefore, If x is 5 then the other two numbers are :

x+2 = 5+2 =≥ 7

x+4 = 5+4 =≥ 9

Method 2 :

By subtracting 3 from the RHS,

x + x+2 + x+4 = 24 - 3

adding all the variables and constants,

3x + 6 = 21

Transposing 6 to the RHS so all the variables are on one side and constants on the other,

3x = 21 - 6

3x =  15

Transposing 3 to the RHS,

Hence the numbers are 5,7 and 9.

Verification :-

Let us verify the answer.

sum :

5+7+9 = 21

21 + 3 = 24

(or)

21 = 24 - 3

LHS = RHS

Hence verified.