SOLUTION: The sum of two numbers is 39 and their difference is 7. What are the numbers?

Question 114504: The sum of two numbers is 39 and their difference is 7. What are the numbers?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

THERE ARE TWO WAYS (MAYBE MORE) TO WORK THIS:
LETS DO THE EASY WAY FIRST, THEN I WILL SET UP THE HARD WAY AND YOU CAN FINISH IT.
Let x=one number
Then 39-x=the other number
Now we are told that:
(39-x)-x=7 get rid of parens (distributive law)
39-x-x=7 subtract 39 from both sides
39-39-x-x=7-39 collect like terms
-2x=-32 divide both sides by -2
x=16-------------------one number
39-x=39-16=23------------the other number
CK
their difference IS 7 and their sum IS 39

THE HARD WAY:
Let x=one number
And y=the other number
x+y=39----------------------------eq1
x-y=7--------------------------eq2
substitute x=39-y from eq1 into eq2 and we get
x-(39-x)=7 get rid of parens
x-39+x=7 add 39 to both sides
x-39+39+x=7+39 collect like terms
2x=46
Now you finish this one

Hope this helps---ptaylor
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