Question

The sum of two numbers is 59 and the difference is 13. What are you numbers

Answer 1

❍ Question -:

The sum of two numbers is 59 and the difference is 13. Find the two numbers

❍ Step-by-step explanation -:

Given :

• Sum of two numbers = 59
• Difference = 13

To Find :

• Two numbers

Assuming :

Let us assume first number as 'x' and second number as 'y'.

Solution :

According to question -:

x + y = 59 (equation 1)

x - y = 13 (equation 2)

On Adding equation 1 and 2 we get

`\large \rm{x + y = 59 } \\ \large \rm{ \underline{x - y = 13}} \\ \large\sf{2x = 72}`

`\large\sf{ 2x = 72}`

`\large \sf{ x = \cancel (72)/(2) }`

`\boxed{\large\rm{x = 36} }`

Now, we will substitute the value of x = 36

x + y = 59

36 + y = 59

y = 59 - 36

y = 23

Verifying -

Equation 1

x + y = 59

substituting the value of x and y

36 + 23 = 59

→ 59 = 59

LHS = RHS

Hence proved.

Equation 2

x - y = 13

substituting the value of x and y

36 - 23 = 13

→ 13 = 13

LHS = RHS

Hence proved.

Final Answer :

• First number = 36
• Second number = 23

`\underline{\rule{182pt}{3pt}}`

Answer 2

Question :

The sum of two numbers is 59 and the difference is 13. What are you numbers ?

Given :

• Sum of two numbers = 59

• Difference of these numbers = 13

To Find :

We have to find the numbers .

Concept :

The concept of this question belongs to equations . We have to find the numbers by making equation . So we must have study of creating equations .

To Assume :

In this question we have to assume both the numbers . So ,

• Let the 1st no. be = x

• Let the 2nd no. be = y

So let's get started with solution :

According to question of sum of two no. is 59 . Therefore ,

• x + y = 59 --------------- ( Equation 1 )

According to question difference of these numbers is 13 . So ,

• x - y = 13 --------------- ( Equation 2 )

Now adding both equation :

• x + y + ( x - y ) = 59 + 13

• x + y + x - y = 72

• 2x = 72

• x = 72/2

• x = 36

Now , putting value of x in equation 1 to get value of y :

• x + y = 59

• 36 + y = 59

• y = 59 - 36

• y = 23

Hence ,

`\boxed{ \sf{ \pink{Value \: of \: x \: and \: y = 36 \: and \: 23 \: respectively}}}`

Verification :

We are verifying our answer by putting values of x and y in equation 1 and equation 2 . So ,

For equation 1 :

• x + y = 59

• 36 + 23 = 59

• 59 = 59

• L.H.S = R.H.S

For equation 2 :

• x - y = 13

• 36 - 23 = 13

• 13 = 13

• L.H.S = R.H.S

Therefore, we can say that our value for x and y are correct .

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