Question

find two numbers whose sum is 95 and whose difference is 31

Answer 1

n order to solve this problem you need to translate the words into mathematical statements.
When a statement says 'a number' we can represent this number with a variable (like 'x' or 'y').
Words like sum and difference are operations in math like add (+) or subtract (-).
And the statement 'is' or 'becomes' represents equals.
Your particular question needs 2 equations (because of the two 'is'). Take a look at this question,

The sum of two numbers is 31 and their difference is 9.
+ = - =
Let x = one number, Let y = other number
x + y = 31, x - y = 9
We now have two equations:
(1) x+y=31
(2) x-y=9
We have to choose one to isolate a variable (a letter),
(2) x-y=9 work on both sides,
x-y +y=9+y
x+0=9+y
x=9+y Now substitute this in the other equation,
(1) x+y=31
(9+y)+y=31 and solve for y,
9 + 2y=31
9-9+2y=31-9
2y=22
2y/2=22/2
y=11 we can sub this into either equation to solve for x,
(2) x-y=9
x-11=9
x-11+11=9+11
x=20
We can check our answers using the original equations:
(1) x+y=31
20+11=?31
31=31 (it checks!)
(2) x-y=9
20-11=?9
9=9 (it checks!)
If we look back to our original equation, one number (x) is 20 and the other number (y) is 11.
Hope this helps.

Answer 2

let the first number be x and second number be y so the equations formed are ,
x+y=95 _________ 1
x-y= 31__________ 2
add 1&2. ( elimination method )

x+y=95
x-y= 31


= 2x=126
x=63
put the value of x as 63 in eq 1 which was.

x+y=95
63+y=95
y=32

the two numbers are 63 and 32