SOLUTION: one number is three times another and their product is equal to their sum increased by fifty five. Find the numbers

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Question 1042713: one number is three times another and their product is equal to their sum increased by fifty five. Find the numbers
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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y=one number; x=another number
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y=3x
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xy=x%2By%2B55
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x%283x%29=x%2B3x%2B55
3x%5E2=4x%2B55
3x%5E2-4x-55=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B-55+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A3%2A-55=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+676+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+676+%29%29%2F2%5C3+=+5
x%5B2%5D+=+%28-%28-4%29-sqrt%28+676+%29%29%2F2%5C3+=+-3.66666666666667

Quadratic expression 3x%5E2%2B-4x%2B-55 can be factored:
3x%5E2%2B-4x%2B-55+=+3%28x-5%29%2A%28x--3.66666666666667%29
Again, the answer is: 5, -3.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-55+%29

x=5.00 or -3.66667
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If x=5:
y=3x
y=3(5)
y=15
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If x=-3.66667
y=3x
y=3(-3.66667)
y=-11
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ANSWER: The two numbers are 5 and 15 or -3.66667 and -11