SOLUTION: Could someone please help me with this problem? I need to solve and show the equation used for the solution: The sum of two numbers is 40. Their difference is 8. Find

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Question 59399This question is from textbook Beginning Algebra
: Could someone please help me with this problem?
I need to solve and show the equation used for the solution:
The sum of two numbers is 40. Their difference is 8. Find the two numbers.
Thanks,
Sher This question is from textbook Beginning Algebra

Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Hi Sher,
Solve and show the equation used for the solution:
The sum of two numbers is 40. Their difference is 8. Find the two numbers.
:
Sum means add and difference means subtract.
Let one number be:x and the other be:y
x+y=40
x-y=8
Add the two equations and the y's are eliminated.
x+y=40
x-y=8
______
2x+0=48
2x=48
2x/2=48/2
x=24
Substitute that in for x in one of the equations and solve for y.
24+y=40
-24+24+y=40-24
0+y=16
y=16
One number is: 24 and the other is 16
If you aren't using two equations and two unknowns yet, let me know and I'll edit this. I know I have answered a lot of your questions. I remember that you were graphing, but I don't remember if you were graphing two lines at the same time.
Happy Calculating!!!

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Could someone please help me with this problem?
I need to solve and show the equation used for the solution:
The sum of two numbers is 40. Their difference is 8. Find the two numbers.
Thanks,
Sher

Using one unknown:

Let the larger number = x

>>...The sum of two numbers is 40...<<

Since 

larger number + smaller number = Sum of both numbers

Smaller number = Sum of both numbers - larger number

so

Smaller number = (40 - x)

>>,,,Their difference is 8...<<

Larger number - Smaller number = 8

                  x - (40 - x) = 8

Solve that and get x = 24

So larger number = x = 24
Smaller number = 40 - x = 40 - 24 = 16

------------------------------------------

Using two unknowns:

Let the larger number = x

Let the smaller number = y

>>...The sum of two numbers is 40...<<

 x + y = 40

>>...Their difference is 8...<<

 x - y = 8

So we have the system of two equations in two unknowns

 x + y = 40
 x - y =  8

Can you solve that system? If not post again asking
how.

x = 24, y = 16
       
Edwin