Question

The sum of two numbers is 9 and the difference is 7. What are the two numbers?

Answer 1

Question :

The Sum of two number is 9 and thier difference is 7, then Find the number.

Answer:

x= 8 and 1.

Step-by-step explanation:

Sum of two number be 9,

Let first number be x and other be y

so,

$\: \: \: \: \: \: \tt x + y = 9.$

and, their difference is 7,

$\: \: \: \: \: \: \tt x - y = 7.$

Solving both equation by putting value,

We get,

$\: \: \: \: \: \: \tt x \cancel{+ y} = 9. \\ \: \: \: \: \: \: \tt x \cancel{- y }= 7 \\ - - - - - - - - - \\ \tt \: \: \: 2x \: \: \: \: \: \: = 16.$

$\: \: \: \: \: \: \: \: \: \: \: \tt x = 8.$

Now, Putting the value in equation 1, we get.

$\tt \: \: \: \: \: \: x + y = 9. \\ \tt \: \: \: \: \: \: 8 + y = 9. \\ \tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 1.$

Therefore, the Value of first number be 8 and other be 1.

Let try other method,

Let first no be x and other number be y,

$\: \: \: \: \: \: \tt \: x + y = 8. - - 1\\ \: \: \: \: \: \: \: \tt x - y = 7. - - 2\\ or \\ \tt \: \: \: \: \: \: x = 7 + y \: \: (from \: 2)$

Putting the value in equation 1, we get

$\tt \: \: \: \: \: \: x + y = 9. \\ \tt \leadsto 7 + y + y = 9. \\ \tt \leadsto2y = 2. \\ \tt \leadsto y = 1.$

Now, putting in equation 2,

$\tt \: \: \: \: \: \: x = 7 + y \\ \tt \leadsto x = 7 + 1. \\ \tt \leadsto x = 8.$

Therefore, again the value of both numbers be 8 and other be 1.

Answer 2

$\huge{\bold{ Solution}} \\ \\ Let \: the \: two \: numbers \: be \: a \: and \: b. \\ \\ According \: to \: question:- \: \\ sum \: of \: two \: number \: is \: 9. \\ a + b = 9 - (1) \\ and \: their \: difference \: is \: 7. \\ so \: a - b = 7 - (2) \\ \\ adding \: equ. \: (1) \: and \: (2) \\ a + b + a - b = 9 + 7 \\ 2a = 16 \\ a = 8 \\ Now \: putting \: the \: value \: of \: a \: = 8 \: in \: equ. \: (1) \\ a + b = 9 \\ 8 + b = 9 \\ b = 9 - 8 \\ b = 1 \\ \\ <strong>T</strong><strong>herefore \: the \: numbers \: are \: 8\: and \: 1.$