Question

Sum of two number is 35 and their difference is 13 Find the numbers

Answer 1

Given:-

Sum of two numbers is 35

Their difference is 13

Let the two numbers be x and y

According to question sum of two numbers is

x + y = 35___ eq(1)

And their difference is x – y = 13___ eq(2)

On Adding equation 1 and 2 we get

x + y = 35

x – y = 13

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2x = 48

x = $\frac{48}{2}$

x = 24

According to equation 1,

x + y = 35

24 + y = 35

y = 35 – 24

y = 11

$\bf The \: numbers \: are \: 24 \: and \: 11 \: [Ans]$

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Answer 2

Answer:

Given : The sum of two numbers is 35 and their difference is 13.

Need To Find : The two numbers.

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❍ Let's consider two numbers be x and y .

⠀⠀⠀⠀⠀Case I : The sum of two numbers is 35 .

⠀⠀⠀⠀⠀$\sf{\implies {\therefore \: x + y = 35 }}$

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {\bf{ \:\Bigg( x + y = 35 \Bigg) \qquad\quad\qquad...Eq. \:1 }}}$

⠀⠀⠀⠀⠀Case II : The Difference between two numbers is 13 .

⠀⠀⠀⠀⠀$\sf{\implies {\therefore \: x - y = 13 }}$

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {\bf{\Bigg( \: x - y = 13 \Bigg) \qquad \qquad\quad...Eq.\:2}}}$

⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: By \: Doing\:Elimination\:method \:with\: Eq.\:1 \:and\:\:Eq.\:2 \::}}}$

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {\bf{ \:\Big( x + y =35 \Big) \qquad\quad\qquad...Eq. \:1 }}}$

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {\bf{\Bigg( \: x - y = 15 \Bigg) \qquad \qquad\quad...Eq.\:2}}}$

⠀⠀⠀⠀⠀⠀⠀$\begin{array}{ c c c } x & \cancel{+ y } &= 35 \\ x & \cancel {-y} & = 13\\ --&--&-- \\ 2x&\:= \:& 48 \end{array}$

⠀⠀⠀⠀⠀⠀⠀$:\implies{ \sf{ 2x =\: 48\:}}$

⠀⠀⠀⠀⠀⠀⠀$:\implies{ \sf{ x \:= \dfrac{\cancel {48}}{\cancel {2}}\:}}$

⠀⠀⠀⠀⠀⠀⠀$\boxed{\pink{ \sf{x =\:24}}}\:\bf{\bigstar}$

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⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: Putting \:x=24\:in\: Eq.\:1 \: \::}}}$

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {\bf{\Bigg( \: x - y = 13 \Bigg) \qquad \qquad\quad...Eq.\:2}}}$

⠀⠀⠀⠀⠀⠀⠀$:\implies{ \sf{ 24 - y =\: 13\:}}$

⠀⠀⠀⠀⠀⠀⠀$:\implies{ \sf{ y =\:24 - 13\:}}$

⠀⠀⠀⠀⠀⠀⠀$\boxed{\pink{ \sf{y =\:11}}}\:\bf{\bigstar}$

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Therefore,

• ⠀$\therefore\underline{\pink{ \sf{Hence\:the\:two\;numbers\:are\:24\:and\:11\:.}}}\:\bf{\bigstar}$

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