Question

29. i) The sum of three consecutive numbers is 135. Form a linear equation and
solve it to find all the numbers.
ii) Solve the given equation for value of m :-
3(m + 6) + 2(m + 1) = 45

Answer 1

Answer:

i] 66, 67, 68

ii] m = 5

Step-by-step explanation:

Answer 2

$\huge \color{red} \bf \underbrace{\sf Question } \: 1 \: :$

The sum of three consecutive numbers is 135. Form a linear equation and

solve it to find all the numbers.

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,

Hence,Three consecutive numbers are 44, 45, 46.

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$\huge \color{red} \bf \underbrace{\sf Question } \: 2 \: :$

• 3(m + 6) + 2(m + 1) = 45

Answer :

$\large \sf \implies m = 5$

Solution :

Let's solve ,

• Open brackets by multiplying :

$\sf \implies 3m + 18 + 2m + 2 = 45$

• Combining like terms :

$\sf \implies 5m + 20 = 45$

• Subtracting 20 from both the sides :

$\sf \implies 5m + \cancel{20} \: \: \cancel{-20}= 45 -20$

$\sf \implies 5m = 25$

• Dividing both sides by 5 :

$\sf \implies \frac{\cancel{5}\: m}{\cancel{5}} = \frac{25}{5}$

$\sf \implies \boxed{\mathfrak{ \: \:m = 5\: \:}}$

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