Question

29. i) The sum of three consecutive numbers is 135. Form a linear equation and
solve it to find all the numbers.

Answer 1

Answer :-

• The three consecutive numbers are 44, 45 and 46.

Given :-

• The sum of three consecutive numbers is 135.

To find :-

• The numbers.

Step-by-step explanation :-

• In this question, it has been given that the sum of three consecutive numbers is 135. We have to form a linear equation using this information and solve it to find all the numbers.

Calculations :-

• We know that consecutive numbers don't have any gap between them, that is, they are continous.

• So, let the three numbers be x, (x + 1) and (x + 2)

• Now, it has been given that their sum is 135.

• That means, the sum of x, (x + 1) and (x + 2) is 135.

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$\sf \implies x + (x + 1) + (x + 2) = 135$

Removing the brackets,

$\sf \implies x + x + 1 + x + 2 = 135$

Keeping the variables and constants separately in brackets,

$\sf \implies (x + x + x) + (1 + 2) = 135$

On simplifying,

$\sf\implies 3x + 3 = 135$

Transposing 3 from LHS to RHS, changing it's sign,

$\sf\implies 3x = 135 - 3$

Subtracting 3 from 135,

$\sf\implies 3x = 132$

Transposing 3 from LHS to RHS, changing it's sign,

$\sf \implies x = \dfrac{132}{3}$

Dividing 132 by 3,

$\sf \implies x = 44.$

• The value of x is 44.

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Hence, the numbers are as follows :-

$\bf x = 44.$

$\bf x + 1 = 44 + 1 = 45.$

$\bf x + 2 = 44 + 2 = 46.$

Answer 2

Answer :

➠ Three consecutive numbers are 44, 45, 46.

Solution :

Given :

• Sum of three consecutive numbers is 135.

To Find :

• Three consecutive numbers whose sum is 135.

According to question :

• It is given that 3 numbers are convective. Hence , they are continuous.
• Sum of these 3 consecutive numbers is 135.
• We have to form a linear equation.

Let 3 consecutive numbers be x , (x +1) and (x + 2).

So,

Our equation will be :

$\implies \sf x + (x + 1) + (x +2 ) = 135$

• Removing brackets :

$\implies \sf x + x + 1 + x +2 = 135$

• Combining like terms :

$\implies \sf 3x + 3 = 135$

• Subtracting 3 from both the sides :

$\implies \sf 3x + \cancel{\: \: 3 \: } \: \: \: \red{\cancel{-3}} = \color{black}135\red{{-3}}$

$\implies \sf 3x = 132$

• Dividing both sides by 3 :

$\implies\large \sf \frac{\cancel{3} \: x}{\cancel{3}} = \frac{132}{3}$

$\implies \sf \large \boxed{\mathfrak{\: \: x = 44\: \:}}$

So,

• First number = x

$\: \: \: \: \: \: \: \: \: \: \: \: \implies \sf 44$

• Second number = (x + 1)

$\: \: \: \: \: \: \: \: \: \: \: \:\implies \sf ( 44 + 1 )$

$\: \: \: \: \: \: \: \: \: \: \: \:\implies \sf 45$

• Third number = ( x + 2)

$\: \: \: \: \: \: \: \: \: \: \: \:\implies \sf ( 44 + 2 )$

$\: \: \: \: \: \: \: \: \: \: \: \:\implies \sf 46$

Hence,

Three consecutive numbers are 44, 45, 46.

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