SOLUTION: find two positive numbers so that twice their sum euals their product and one number is 10 times the other number

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Question 159192: find two positive numbers so that twice their sum euals their product and one number is 10 times the other number
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
find two positive numbers so that twice their sum equals their product and one number is 10 times the other number
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Let the numbers be x and 10x
EQUATION:
2(x + 10x) = x(10x)
22x = 10x^2
5x^2 - 11x = 0
x(5x-11) = 0
x = 0 or x = (11/5)
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If x = 0, 10x = 0 ( not two different so not the solution to the problem)
If x = (11/5), 10x = 22
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Two numbers x & y
Write an equation for each statement:
;
find two positive numbers so that twice their sum equals their product
2(x+y) = xy
2x + 2y = xy
:
and one number is 10 times the other number
x = 10y
:
Substitute 10y for x in the 1st equation, find y
2(10y) + 2y = y(10y)
;
20y + 2y = 10y^2
;
22y = 10y^2
:
0 = 10y^2 - 22y
Factor
2y(5y - 11) = 0
:
5y = +11
y =
y = 2.2
then
x = 10(2.2)
x = 22
;
;
Check solutions in the 1st equation:
2(22 + 2.2) = 22*2.2
2(24.2) = 48.4
48.4 = 48.4