SOLUTION: The age of a father is triple the son. 5 years later the product of their ages will be 1000. Find their present ages.

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Question 956013: The age of a father is triple the son. 5 years later the product of their ages will be 1000. Find their present ages.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
F=father's age; S=son's age
F=3S
%28F%2B5%29%28S%2B5%29=1000 Substitute for F.
%283S%2B5%29%28S%2B5%29=1000
3S%5E2%2B20S%2B25=1000 Subtract 1000 from each side.
3S%5E2%2B20S-975=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aS%5E2%2BbS%2Bc=0 (in our case 3S%5E2%2B20S%2B-975+=+0) has the following solutons:

S%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=%2820%29%5E2-4%2A3%2A-975=12100.

Discriminant d=12100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+12100+%29%29%2F2%5Ca.

S%5B1%5D+=+%28-%2820%29%2Bsqrt%28+12100+%29%29%2F2%5C3+=+15
S%5B2%5D+=+%28-%2820%29-sqrt%28+12100+%29%29%2F2%5C3+=+-21.6666666666667

Quadratic expression 3S%5E2%2B20S%2B-975 can be factored:
3S%5E2%2B20S%2B-975+=+3%28S-15%29%2A%28S--21.6666666666667%29
Again, the answer is: 15, -21.6666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B20%2Ax%2B-975+%29

So S=15 ANSWER 1: The son is 15 years old.
F=3S=3(15yrs)=45yrs ANSWER 2: The father is 45 years old.
CHECK:
%28F%2B5%29%28S%2B5%29=1000
%2845%2B5%29%2815%2B5%29=1000
%2850%29%2820%29=1000
1000=1000