SOLUTION: I don't know what type of help I need. I am trying to solve the problem - the product of two numbers is 442. The sum of the two numbers is 43. Find the two numbers. I don't kno

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Question 683060: I don't know what type of help I need. I am trying to solve the problem - the product of two numbers is 442. The sum of the two numbers is 43. Find the two numbers. I don't know if this is algebra or what it is. I tried timesing 43 by several numbers and I tried dividing 442 but I can't find an answer.
Found 4 solutions by ReadingBoosters, stanbon, Edwin McCravy, Alan3354:
Answer by ReadingBoosters(3246)   (Show Source): You can put this solution on YOUR website!
x is one number
y is the other number
...
xy=442
x+y=43 ==> rearrange as x = 43-y
...
Substitution
(43-y)y = 442

...
Either determine that
factors as (y-26)(y-17)=0
y = 26 AND y = 17
Or
Solve for y with the Quadratic Formula

y =
y =
y =
y =
...
y =
y =
...
Check
26*17 = 442
26+17=43
...
The two numbers are 26 and 17.
.....................
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Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
the product of two numbers is 442. The sum of the two numbers is 43. Find the two numbers.
-------
Equations:
xy = 442
x+y = 43
-----
Substitute for "x" and solve for "y":
x = 43-y
----
So (43-y)y = 442
-y^2 +43y = 442
-----
y^2 - 43y +442 = 0
(y-17)(y-26) = 0
y = 17 or y = 26
------
Solve for "x":
If y = 17, x = 43-17 = 26
If y = 26, x = 43-26 = 17
===================
Cheers,
Stan H.
===============
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
I think the best way is to break 442 into its prime factors:

442 = 2×13×17

The prime factors are 2,13, and 17
So there are three pairs you can make by grouping two of them
and taking the product of the two grouped times the third:

2×(13×17) = 2×221, and the sum of 2+221 is 223, not 43
(2×17)×13 = 34×13, and the sum of 34+13 is 47, not 43.
(2×13)×17 = 26×17, and the sum of 26+17 is 43, so the answer is 26 and 17.

Edwin
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I don't know what type of help I need. I am trying to solve the problem - the product of two numbers is 442. The sum of the two numbers is 43.
-------------
442 has only 3 integer factors, 2, 13 & 17
It's either:
2*221
26*17
13*34
-----
only 26 + 17 = 43
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