# SOLUTION: A father's age is 3 more than four times the age of his son. If the product of their ages is 351, what is the father's age?

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Age -> SOLUTION: A father's age is 3 more than four times the age of his son. If the product of their ages is 351, what is the father's age?      Log On

 Ad: Over 600 Algebra Word Problems at edhelper.com Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Word Problems: Age Solvers Lessons Answers archive Quiz In Depth

Question 253251: A father's age is 3 more than four times the age of his son. If the product of their ages is 351, what is the father's age?
Found 2 solutions by Greenfinch, JimboP1977:
You can put this solution on YOUR website!
If the son is Z years old, the father is 4Z + 3 years old
Product is Z(4Z + 3) = 4Z^2 + 3Z = 351
So 4Z^2 + 3Z - 351 = 0
You can plug into the formula now or try factorisation
Factors of 351 are 3x3x3x13
3 x 13 gives 39 and 3 x 3 is 9, multiplied by the 4 from the z^2 term gives 36, difference 3 which is the Z term so
(4Z + 39)(Z - 9)=0
Z = -39 or 9
So son's age is 9, father's age is 39

You can put this solution on YOUR website!
Father's Age = F
Son's Age = S

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=5625 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9, -9.75. Here's your graph:

Son's age is 9, Father's age is 39