SOLUTION: The sum of two number is 40. Their difference is 8. Find the two numbers.

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Question 99810This question is from textbook Beginning algebra sixth edition
: The sum of two number is 40. Their difference is 8. Find the two numbers. This question is from textbook Beginning algebra sixth edition

Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
First lets give each number a variable
We will call one number x
and the other number we will call y
Given: the sum of two numbers is 40 so
x%2By=40
Given: their difference is 8 so
x-y=8
Now take the first equation x%2By=40 and set it equal to x
To do this subtract y from both sides of the equal sign
x%2By=40
x%2By-y=40-y
x%2B0=40-y
x=40-y
Now take the second equation x-y=8 and replace the x with 40-y
x-y=8
40-y-y=8
40-2y=8
-2y=8-40
-2y=-32
y=16
So now that we have found y equals 16 we can replace the y in either of our original equations and solve for x
x%2By=40
x%2B16=40
x=40-16
x=24
Now we have found the two numbers
x=24 and y =16
Check these by trying them in both of the original equations so
x%2By=40
24%2B16=40
40=40
and the other
x-y=8
24-16=8
8=8
They both work so we know we have correctly found the numbers.