SOLUTION: One number is twice the other and their product is equal to six times the larger.Find the numbers

Question 523466: One number is twice the other and their product is equal to six times the larger.Find the numbers
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = 2y
.
Note that that means x > y.
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The product = 6 times the greater number.
.
x*y = 6x
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Substitute x = 2y
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2y*y = 6(2y)
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2y^2 -12y = 0
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2y(y-6) = 0
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y = 0 or 6
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Zero works quite nicely. Zero times anything is zero. So, x*0 = 6*x is true. In this case, x can be any number from -infinity to +infinity. This means there is no ordered pair. (x,0) for any x. This probably is a spurious solution, which means it is one that is not relevant to the practical problem at hand.
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But how about y=6?
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x = 2y
x = 2(6)
x = 12
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Their product = 12*6 = 72.
6*12 = 72.
Correct.
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Answer: The two numbers are 6 and 12.
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Done.
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!
One number is twice the other and their product is equal to six times the larger.Find the numbers

Let the larger number be = L, and smaller, S

Then we can say that: L = 2S

Also, LS = 6L ----- Dividing by GCF, L gives us: S, or smaller no. as:

Therefore, L, or larger no. = (2 * 6)

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