Question

26)
If sum of 4 consecutive natural odd numbers is 32 then find smallest number​

Answer 1

Given :

• Sum of 4 consecutive natural odd numbers = 32

To find :

• Smallest number.

Solution :

Let the number be x

Here,

The four natural odd numbers with variables are :

• x
• x + 2
• x + 4
• x + 6

Sum of these = 32

Equation will be :-

• x + x + 2 + x + 4 + x + 6 = 32

Calculations :-

$\bf \implies x + x + 2 + x + 4 + x + 6 = 32 \\ \\ \bf \implies4x + 12=32 \\ \\ \bf \implies 4x = 32 - 12 \\ \\ \bf \implies 4x = 20 \\ \\ \bf \implies x = \dfrac{20}{4} \\ \\ \bf \implies x = 5$

Therefore, The smallest number is 5.

Other odd natural number are :-

• x + 2 = 5 + 2 = 7
• x + 4 = 5 + 4 = 9
• x + 6 = 5 + 6 = 11

All 4 numbers are, 5,7, 9,11.

Verification :-

$\bf \implies x + x + 2 + x + 4 + x + 6 = 32 \\ \\ \bf \implies 5 + 5 + 2 + 5 + 4 + 5 + 6 = 32 \\ \\ \bf \implies 32 = 32 \\ \\ \bf LHS = RHS \\ \\ \bf Hence, Verified.$

Answer 2

Given :-

• Sum of 4 consecutive natural odd number = 32

To find :-

• Smaller number.

Solution :-

• Let the number be x

Here,

• The four natural odd numbers with variables are :

• ${\tt{x}}$
• ${\tt{x + 2}}$
• ${\tt{x + 4}}$
• ${\tt{x + 6}}$

Sum of these = 32

Equation will be :

• ${\tt{x + x + 2 + x + 4 + x + 6 = 32}}$

Calculations :

:$\implies{\sf{x + x + 2 + x + 4 + x + 6 = 32}}$

$\: \: \: \: \:$:$\implies\bf$${\sf{4x + 12 = 32}}$

$\: \: \: \: \: \: \: \: \:$:$\implies\sf$${\sf{4x = 32 - 12}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$:$\implies\sf$${\sf{4x = 20}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$:$\implies\sf$${\bf{x = \frac{20}{4}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$:$\implies\bf$$\boxed{\bf\underline\red{x = 5}}$ $\large{\bf\green{✓}}$

Therefore, are smallest number is 5.

Other odd natural number are :

• ${\tt{x + 2 = 5 + 2 = 7}}$
• ${\tt{x + 4 = 5 + 4 = 9}}$
• ${\tt{x + 6 = 5 + 6 = 11}}$

All 4 numbers are , 5 , 7 , 9 , 11.

★ ${\boxed{\boxed{\rm{Verification}}}}$ $\large{\bf\green{✓}}$

:$\implies{\sf{x + x + 2 + x + 4 + x + 6 = 32}}$

:$\implies{\sf{5 + 5 + 2 + 5 + 4 + 5 + 6 = 32}}$

$\: \: \: \:\:\:\:\:\: \:\:\:\: \: \: \: \: \: \: \:$:$\implies\bf$ $\boxed{\bf\underline\green{32 = 32}}$ $\large{\bf\green{✓}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$ $\large{\bf\green{★}}$${\boxed{\boxed{\bf{LHS = RHS}}}}$ $\large{\bf\red{★}}$

$\: \: \: \: \: \: \: \: \: \:$ $\large{\bf\red{★}}$${\boxed{\boxed{\bf{Hence Verified,}}}}$ $\large{\bf\green{★}}$