SOLUTION: what two numbers added together that equals 70 but when multiplied it equals 600

Question 284176: what two numbers added together that equals 70 but when multiplied it equals 600

Found 3 solutions by Alan3354, solver91311, stanbon:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
They have to be even numbers.
If they were both odd, the product would be odd.
If one were odd and one even, the sum would be odd.
--------------------------------
They have to be multiples of 10.
The 2 LS digits are 00. If they're not multiples of 10, then one of the numbers is 25, but it's already been determined that both number are even.
That makes the problem:
what two numbers added together that equals 7 but when multiplied it equals 6?
That factors of 6 are 1 & 6, or 2 & 3
1 + 6 = 7
--> 10 & 60

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let represent one of the numbers. Let represent the other number.

Then:

which is to say:

Then

Which is to say:

Just solve for . One of the roots will be one of the numbers, and the other root will be the other number.

John

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
what two numbers added together that equals 70 but when multiplied it equals 600
---------------------------------
Equation:
x + y = 70
xy = 600
------------------
y = 70-x
---
Substitute and solve for "x":
x(70-x) = 600
70x -x^2 = 600
x^2-70x+600 = 0
---
Factor:
(x-10)(x-60) = 0
---
If x = 10, y = 60
If x = 60, y = 10
=========================
Cheers,
Stan H.
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