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?

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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:
Answer by Greenfinch(383) About Me  (Show Source):
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

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Father's Age = F
Son's Age = S
F-3=4S%0D%0A%7B%7B%7BFS=351
F=351%2FS
F-3=%28351%2FS%29-3=4S
%28351%2FS%29-3=4S
%28%28351-3S%29%2FS%29=4S
351-3S=4S%5E2
0=4S%5E2%2B3S-352
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B3x%2B-351+=+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=%283%29%5E2-4%2A4%2A-351=5625.

Discriminant d=5625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+5625+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+5625+%29%29%2F2%5C4+=+9
x%5B2%5D+=+%28-%283%29-sqrt%28+5625+%29%29%2F2%5C4+=+-9.75

Quadratic expression 4x%5E2%2B3x%2B-351 can be factored:
4x%5E2%2B3x%2B-351+=+4%28x-9%29%2A%28x--9.75%29
Again, the answer is: 9, -9.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-351+%29


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