Question

(3 marks
Sum of two number is 45 and the greater numbe
is twice the smaller number. Find the numbers​

Answer 1

Given : Sum of two number is 45 and the greater number is twice the smaller number .

Exigency to find : The Numbers.

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❍ Let's Consider the smaller number be x .

Given that ,

• The greater number is twice the smaller number .

Therefore,

• Greater Number is 2x .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: to \: Given \: Question \::}}$

⠀⠀━━━ Sum of two number is 45 .

$\qquad \longmapsto \sf x + 2x = 45$

$\qquad \longmapsto \sf 3x = 45$

$\qquad \longmapsto \sf x = \cancel{\dfrac{45}{3}}$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 15 }} }\bigstar$

Therefore,

• Smaller number is x = 15
• Greater number is 2x = 2(15) = 30 .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:The \:two\:Numbers \:are\:\bf{15 \: \& \: 30 .}}}}$

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V E R I F I C A T I O N :

Given that ,

⠀ Sum of two number is 45 .

As , We know that ,

• Two numbers are 15 & 30 .

$\qquad \longmapsto \sf 15 + 30 = 45$

$\qquad \longmapsto \frak{\underline{\purple{\:45 = 45 }} }\bigstar$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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Answer 2

It is given that:

• The sum of two numbers is 45.
• The first number is twice the second number.

We have to find: The value of the two numbers, respectively.

Solution:

Let us assume that the value of second number be "m". So that, the value of the first number will be "2m", since it is twice the first number.

As it is given that the sum of the two numbers is 45, here forms the equation,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf \pmb{2m + m = 45}}}$

Now, if we solve this equation, we can obtain the value of "m". And with that value, we will be able to find the actual value of the two numbers. Let us solve the equation!

$\dashrightarrow{ \sf{2m + m = 45}} \\ \\ \dashrightarrow{ \sf{3m = 45}} \\ \\ \dashrightarrow{ \sf{m = \dfrac{45}{3} }} \\ \\ \dashrightarrow{ \sf{m = \dfrac{ \cancel3 \times 15}{ \cancel3 \times 1} }} \\ \\ \dashrightarrow{ \sf{m = \dfrac{15}{1} }} \\ \\ \dashrightarrow \underline{ \sf \pmb{m = \tt15}}$

We've obtained the value of "m", but before proceeding with the next step, let us confirm the value of "m" by verifying it!

• Substituting the obtained value of "m" in the equation formed.

$\longmapsto{ \sf{2m + m = 45}} \\ \\ \longmapsto{ \sf{2( \purple{15}) + \purple{15} = 45}} \\ \\ \longmapsto{ \sf{30 + 15 = 45}} \\ \\ \longmapsto{ \sf{45 = 45}}$

LHS equals RHS, hence the value of "m" is correct!

Now, on substituting the value of "m" in the expressions formed for the numbers:

$\\ \Rightarrow{ \sf{ \pmb{First \: number} \: i.e., \: 2m = 2(15) = \underline{\boxed{\frak{ \red{\pmb{30}}}}}}} \\ \\ \Rightarrow{ \sf{ \pmb{Second \: number} \: i.e., \: m = \underline{\boxed{\frak{ \red{\pmb{15}}}}}}}$

$\\ \therefore \underline{ \sf {The \: two \: numbers \: are \: \tt{30} \: and\: \tt{15}\sf{, \: respectively.}}}$

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