The sum of two numbers is 36. Their difference is 14. What are the two numbers?

Answer 1

The two numbers we'll call x and y. Let's set up equations to model the situation:


x+y=38
x-y=14

Solving the second one for x,
x=y+14

Plug this into the first equation for x and get:

(y+14)+y=36
2y+14=36
2y=36-14
2y=22
y=11

x-y=14
x-11=14
x=14+11
x=25

The two numbers are 11 and 25.

Hope this helps.

Answer 2

Let the larger number equal x, and the smaller number = y.
Given:
x + y = 36
x - y = 14
If we add these two equations together, we get:
(x + x) + (y - y) = (36 + 14)
2x + 0 = 50
2x = 50
x = 25

Now substitue the value for x into one of the original equations:
(25) + y = 36 --- Subtract 25 from both sides...
y = 11

Answer: 25 and 11

Check:
25 + 11 = 36
36 = 36 --- Checks out!

25 - 11 = 14
14 = 14 ---- Checks out!

Answer 3

Let the two numbers be X and X + 14.

Then X + X + 14 = 36

or 2X + 14 = 36

or 2X = 22

or X = 11

If X = 11, then X + 14 = 25.

The two numbers are 11 and 25.

I hope I'm not just giving you an answer for you to plug into your homework, but that you'll take a look at this and see how to get the answer.

Answer 4

call one of the numbers x. since the difference is 14, the second number will be (x+14). the sum is 36 so:
x + (x+14) = 36
x+x+14 = 36
2x + 14 = 36
2x = 22
x = 11
one is 11, and the other is 11 + 14 = 25

Answer 5

25 and 11

Answer 6

11 & 25

Answer 7

let x and y be the two unknown numbers

set up a system of equations

x + y = 36
x - y = 14

add these two equations together so y will cancel out

2x = 50
x = 25

plug x back into one of the equations to find y

x - y = 14
25 - y = 14
y = 11

thus the answer is

x = 25
y = 11

Answer 8

11 & 25

Answer 9

x+y =36
x-y =14

adding the two equations 2x =50 x=25 and substituing x in one of the two y =11

resume x=25 y =11

Answer 10

x + y = 36 (simultaneous equations = add the 2 equations)
x - y = 14 +
________
2x = 50
x = 25

x + y = 36
25 + y = 36
y = 11

numbers are 11 and 25