Question

the defference between two natural number is 10 and their sum is 56 find the number ​

Answer 1

Question:-

the difference between two natural number is 10 and their sum is 56 find the number

Answer:-

• The two numbers are 23 and 33 respectively.

To find:-

• The two numbers

Solution:-

• Let the first number = x
• Let the second number = y
• Sum = 56
• Difference = 10

We have to make two equations

• x + y = 56 ......(1)
• x – y = 10........(2)

Solve eq 1,

$\large{ \tt : \implies \: \: \: \: x + y = 56}$

$\large{ \tt : \implies \: \: \: \: x = 56 - y}$

Put the value of x in eq 2,

$\large{ \tt : \implies \: \: \: \: (56 - y) - y = 10}$

$\large{ \tt : \implies \: \: \: \: - 2y = 10 - 56}$

$\large{ \tt : \implies \: \: \: \: - 2y = - 46}$

$\large{ \tt : \implies \: \: \: \: y = \frac{ - 46}{ - 2} }$

$\large{ \tt : \implies \: \: \: \: y = 23}$

Put the value of y in eq 1,

$\large{ \tt : \implies \: \: \: \: x + 23 = 56}$

$\large{ \tt : \implies \: \: \: \: x = 56 - 23}$

$\large{ \tt : \implies \: \: \: \: x = 33}$

Hence,

The two numbers are 23 and 33 respectively.