Question

a) 24 and 11 b) 25 and 12 c) 20 and 15 14. The sum of two numbers is 35 and their difference is 13. The numbers are
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Answer 1

Answer:

a) 11 & 24

Step-by-step explanation:

As per the provided information in the given question, we have :

• Sum of two numbers is 35.
• Their difference is 13.

We are asked to find the numbers.

In order to find the numbers, firstly let us assume those numbers as two variables, say x and y respectively.

Now, according to the statements stated in the question, we have to frame equations to find the value of x and y. According to the first statement, the sum of the two numbers is 35. Writing it in the form of an equation,

$\longmapsto\rm { x + y = 35 \bf { \dots (1)} }$

And, according to the second statement, their difference is 13. Writing it in the form of an equation,

$\longmapsto\rm { x - y = 13 }$

Transposing -y from L.H.S to R.H.S. So, from this equation, we can say that :

$\longmapsto\rm { x = 13 + y \bf { \dots (2)} }$

Now, substitute the value of x from equation (2) to equation (1).

$\longmapsto\rm { x + y = 35 }$

Substitution of the values.

$\longmapsto\rm { 13 + y + y = 35 }$

Performing the addition of the like terms.

$\longmapsto\rm { 13 + 2y = 35 }$

Transposing 13 from L.H.S to R.H.S, its sign will get changed.

$\longmapsto\rm { 2y = 35 - 13 }$

Performing subtraction in R.H.S.

$\longmapsto\rm { 2y = 22 }$

Transposing 2 from L.H.S to R.H.S, the arithmetic operator before it will get changed.

$\longmapsto\rm { y =\cancel{\dfrac{ 22 }{2} }}$

Dividing 22 by 2.

$\longmapsto\bf { y = 11}$

The second number is 11. Substitute the value of y in the equation (2) to calculate the value of x.

$\longmapsto\rm { x = 13 + y \bf { \dots (2)} }$

Substitution of the value of y.

$\longmapsto \rm { x = 13 + 11}$

Performing addition in R.H.S.

$\longmapsto\bf{ x = 24}$

∴ The numbers are 11 and 24.

Answer 2

Answer:

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11 And 24

$\huge\mathcal{\fcolorbox{aqua}{azure}{\red{✿Explanation ♡❖}}}$

As per the provided information in the given question, we have :

Sum of two numbers is 35.

Their difference is 13.

We are asked to find the numbers.

In order to find the numbers, firstly let us assume those numbers as two variables, say x and y respectively.

Now, according to the statements stated in the question, we have to frame equations to find the value of x and y. According to the first statement, the sum of the two numbers is 35. Writing it in the form of an equation,

$\begin{gathered}\longmapsto\bf{ x = 24}\\ \end{gathered}⟼x=24$

And, according to the second statement, their difference is 13. Writing it in the form of an equation,

$\begin{gathered}\longmapsto\rm { x - y = 13 }\\ \end{gathered}⟼x−y=13$

Transposing -y from L.H.S to R.H.S. So, from this equation, we can say that :

$\begin{gathered}\longmapsto\rm { x = 13 + y \bf { \dots (2)} }\\ \end{gathered}⟼x=13+y(2)$

Now, substitute the value of x from equation (2) to equation (1).

$\begin{gathered}\longmapsto\rm { x + y = 35 }\\ \end{gathered}⟼x+y=35$

Substitution of the values.

$\begin{gathered}\longmapsto\rm { 13 + y + y = 35 }\\ \end{gathered} ⟼13+y+y=35$

Performing the addition of the like terms.

$\begin{gathered}\longmapsto\rm { 13 + 2y = 35 }\\ \end{gathered}⟼13+2y=35$

Transposing 13 from L.H.S to R.H.S, its sign will get changed.

$\begin{gathered}\longmapsto\rm { 2y = 35 - 13 }\\ \end{gathered} ⟼2y=35−13$

Performing subtraction in R.H.S.

$\begin{gathered}\longmapsto\rm { 2y = 22 }\\ \end{gathered}⟼2y=22$

Transposing 2 from L.H.S to R.H.S, the arithmetic operator before it will changed

$\begin{gathered}\longmapsto\rm { y =\cancel{\dfrac{ 22 }{2} }}\\ \end{gathered}⟼y=222$

Dividing 22 by 2.

$\begin{gathered}\longmapsto\bf { y = 11}\\ \end{gathered} ⟼y=11$

The second number is 11. Substitute the value of y in the equation (2) to calculate the value of x.

$\begin{gathered}\longmapsto\rm { x = 13 + y \bf { \dots (2)} }\\ \end{gathered} ⟼x=13+y…(2)$

Substitution of the value of y.

$\begin{gathered}\longmapsto \rm { x = 13 + 11}\\ \end{gathered} ⟼x=13+11$

Performing addition in R.H.S.

$\begin{gathered}\longmapsto\bf{ x = 24}\\ \end{gathered} ⟼x=24$

∴ The numbers are 11 and 24.

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