SOLUTION: (1) A woman is 35years old and her son is 25years old how many years ago was their product is their ages is 1740? (2) A number is subtracted from 20 and from 17. The product o

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Question 407981: (1) A woman is 35years old and her son is 25years old how many years ago was their product is their ages is 1740? (2) A number is subtracted from 20 and from 17. The product of the numbers obtain is 180. Find the original number?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(1) A woman is 35years old and her son is 25years old how many years ago was their product is their ages is 1740?
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x*(x+10) = 1740
x%5E2+%2B+10x+-+1740+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B-1740+=+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=%2810%29%5E2-4%2A1%2A-1740=7060.

Discriminant d=7060 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+7060+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+7060+%29%29%2F2%5C1+=+37.0119030752
x%5B2%5D+=+%28-%2810%29-sqrt%28+7060+%29%29%2F2%5C1+=+-47.0119030752

Quadratic expression 1x%5E2%2B10x%2B-1740 can be factored:
1x%5E2%2B10x%2B-1740+=+%28x-37.0119030752%29%2A%28x--47.0119030752%29
Again, the answer is: 37.0119030752, -47.0119030752. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-1740+%29

It's in the future, when she's 47.012 and he's 37.012.
She had a son at age 10, I don't think algebra is her biggest problem.
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(2) A number is subtracted from 20 and from 17. The product of the numbers obtain is 180. Find the original number?
(20-x)*(17-x) = 180
340+-+37x+-+x%5E2+=+180
x%5E2+%2B+37x+-+160+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B37x%2B-160+=+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=%2837%29%5E2-4%2A1%2A-160=2009.

Discriminant d=2009 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-37%2B-sqrt%28+2009+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2837%29%2Bsqrt%28+2009+%29%29%2F2%5C1+=+3.91093483101497
x%5B2%5D+=+%28-%2837%29-sqrt%28+2009+%29%29%2F2%5C1+=+-40.910934831015

Quadratic expression 1x%5E2%2B37x%2B-160 can be factored:
1x%5E2%2B37x%2B-160+=+%28x-3.91093483101497%29%2A%28x--40.910934831015%29
Again, the answer is: 3.91093483101497, -40.910934831015. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B37%2Ax%2B-160+%29

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