Deep Poopie

Please help if you can. I am 70 years old and trying to help my grand daughter with her math homework. She is in my charge and I have no one else to ask. She is in third grade and I am at a complete loss. She came home with this problem and I am trying to help her solve it with explanation and formula. I have obtained the answer long long hand, but I need a formula to help her to understand. The problem is: Two numbers have a sum of 39, the difference between these two numbers is 11, what are the two numbers. I have derived that the answer is 25+14 (25-11=14) (14+11=25), So I believe the answer is 25+14=39. This is a common sense answer, but not a formulated answer that I can show my grand daughter. I believe that they are calling this type of math (prediction) as per my 7 year old. Can anyone lead me to a web, or perhaps anyone may know this formula. The problem described is one of many, it will take me all night to do the rest using prossess of elimination, Thank you in advance for any help. She is in bed now and I promised her I would have an answer in the morning. I'm in deep :confused:

Yo know:

a + b = 39

a - b = 11

So:

a + b = 39 therefore a = 39 - b

Substituting that into the second equation (a - b = 11) you get:

(39 -b) - b = 11 or 39 - 2b = 11

Thus:

39 = 11 +2b
39 - 11 = 2b
28 = 2b
14 = b
b= 14

Therefore substituting back into a-b = 11

a - 14 = 11
a = 14 +11
a = 25

investigate "basic algebra"

perhaps try here....

http://www.mathleague.com/help/algebra/algebra.htm

Sorry I skipped some steps via assumptions, here is the detailed explanation:

You know:

a + b = 39 and a - b = 11

So:

a + b = 39 (sum of 2 numbers = 39)
a + b - b = 39 - b (subtract b from both sides)
a = 39 -b (+ b and -b on left hand side cancel each other out)

Substituting that into the second equation (a - b = 11) you get:

(39 -b) - b = 11 (substitued value for a into second known equation)
39 - 2b = 11 (-b -b = -2b on left hand side)
39 - 2b + 2b = 11 +2b (add 2b to both sides)
39 = 11 +2b (-2b and +2b on left hand side cancel each other out)
39 - 11 = 11 +2b -11 (subtract 11 from both sides)
39 - 11 = 2b (11 and -11 on right hand side cancel each other out)
28 = 2b (39 - 11 = 28)
28 / 2 = 2b / 2 (divide both sides by 2)
14 = b
b= 14 (swap sides around to see result for b)

Therefore substituting back into a - b = 11

a - 14 = 11
a - 14 + 14 = 11 + 14 (add 14 to both sides)
a = 11 + 14 (-14 and +14 on left side cancel each other out)
a = 25 (11 + 14 = 25)

Thus a = 25 and b = 14

Thank you all. You have been a great help