SOLUTION: If a man is 5 times older than his son, 4 years ago the product of their ages was 52, Now tell their present ages? ( Man? Son?)

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Question 982757: If a man is 5 times older than his son, 4 years ago the product of their ages was 52, Now tell their present ages? ( Man? Son?)

Found 2 solutions by macston, Alan3354:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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M=man; S=son
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M=5S
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(M-4yrs)(S-4yrs)=52yrs
(5S-4yrs)(S-4yrs)=52yrs
5S^2-24S+16=52
5S^2-24S-36=0
(5S+6)(S-6)=0
5S+6=0 or S-6=0
5S=-6 or S=6
S=-5/6 or S=6
ANSWER 1: Son is 6 years old
M=5(S)=5(6yrs)=30 years old
ANSWER 2: The man is 30 years old.
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CHECK:
(M-4yrs)(S-4yrs)=52yrs
(30yrs-4yrs)(6yrs-4yrs)=52yrs
(26yrs)(2yrs)=52yrs
52yrs=52yrs

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If a man is 5 times older than his son, 4 years ago the product of their ages was 52, Now tell their present ages? ( Man? Son?)
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5 times older = a 500% increase in age
= 6 times as old.
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F = 6S
(F-4)*(S-4) = 52
(6S-4)*(S-4) = 52
6S^2 -28S + 16 = 52
3S^2 - 14S - 18 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-14x%2B-18+=+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=%28-14%29%5E2-4%2A3%2A-18=412.

Discriminant d=412 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+412+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+412+%29%29%2F2%5C3+=+5.71629718836407
x%5B2%5D+=+%28-%28-14%29-sqrt%28+412+%29%29%2F2%5C3+=+-1.04963052169741

Quadratic expression 3x%5E2%2B-14x%2B-18 can be factored:
3x%5E2%2B-14x%2B-18+=+%28x-5.71629718836407%29%2A%28x--1.04963052169741%29
Again, the answer is: 5.71629718836407, -1.04963052169741. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-14%2Ax%2B-18+%29

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S =~ 5.716 years
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It's not an integer solution because "5 times older" is not 5 times as old.
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1 time older = ? The same age?
People who don't know what they're talking about should not try to write math books. They should stick to politics.