SOLUTION: Let the daughter's age be x Let the father's age be 4x 3 years ago: Daughter's age = x-3 Father's age = 4x-3 Product of their ages:( x-3)(4x-3)=430 Opening the bracket and app

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Let the daughter's age be x Let the father's age be 4x 3 years ago: Daughter's age = x-3 Father's age = 4x-3 Product of their ages:( x-3)(4x-3)=430 Opening the bracket and app      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 776905: Let the daughter's age be x
Let the father's age be 4x
3 years ago: Daughter's age = x-3
Father's age = 4x-3
Product of their ages:( x-3)(4x-3)=430
Opening the bracket and applying quadratic formula method, we shall have the roots as x= 12.3 and -8.6
So, taking the positive value of x= 12.3years.
Present ages:
Daughter's (x-3)years = 12.3-3 =9.30years (9 years 3 months)
Father's age: (4x-3)years= 4×12.3-3 = 46.21years (46 years 2 months 1day)
Checking:
9.30×46.21= 429.753 = 430 (approximated)
Found 4 solutions by psbhowmick, MathTherapy, Alan3354, sciencetechnologyproductex@yahoo.co.uk:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let father's and daughter's age be x and y years respectively now.

Now:
xy = 430 ________ (1)

3 years before:
x - 3 = 4y
x = 4y + 3 ________ (2)

Substituting x from (2) into (1)
%284y+%2B+3%29y+=+430
4y%5E2%2B3y-430=0

Solve this equation to find y
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 4y%5E2%2B3y%2B430+=+0) has the following solutons:

y%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%2A430=-6871.

The discriminant -6871 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -6871 is + or - sqrt%28+6871%29+=+82.8914953418021.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B430+%29



Imaginary roots suggest that this is impossible. Check and ensure that the data for the question is correct.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
3 years ago a father was 4 times as old as his daughter is now. The product of their ages is 430. Calculate their present ages.

Let daughter's, and father's current ages be D, and F, respectively

Then: F - 3 = 4D ----- F = 4D + 3 ----- eq (i)

Also FD = 430 ------ eq (ii)

D(4D + 3) = 430 ----- Substituting 4D+%2B+3 for F in eq (ii)

4D%5E2+%2B+3D+-+430+=+0

Solve this to get daughter's age. Then find father's: 430%2FD

You should get:

Daughter's current age: highlight_green%2810%29

Father's current age: highlight_green%2843%29

You can do the check!!

Further help is available, online or in-person, for a fee, obviously. Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3 years ago a father was 4 times as old as his daughter is now. The product of their ages is 430. Calculate their present ages.
---------------
F*D = 430
F-3 = 4(D-3)
F = 4D - 9
----
D*(4D-9) = 430
4D^2 - 9D - 430 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-9x%2B-430+=+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=%28-9%29%5E2-4%2A4%2A-430=6961.

Discriminant d=6961 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+6961+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+6961+%29%29%2F2%5C4+=+11.5540759418081
x%5B2%5D+=+%28-%28-9%29-sqrt%28+6961+%29%29%2F2%5C4+=+-9.30407594180808

Quadratic expression 4x%5E2%2B-9x%2B-430 can be factored:
4x%5E2%2B-9x%2B-430+=+%28x-11.5540759418081%29%2A%28x--9.30407594180808%29
Again, the answer is: 11.5540759418081, -9.30407594180808. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-9%2Ax%2B-430+%29

----------------------
D = x
----
Not an integer solution.

Answer by sciencetechnologyproductex@yahoo.co.uk(1) About Me  (Show Source):
You can put this solution on YOUR website!
Let the daughter's age be x
Let the father's age be 4x
3 years ago: Daughter's age = x-3
Father's age = 4x-3
Product of their ages:( x-3)(4x-3)=430
Opening the bracket and applying quadratic formula method, we shall have the roots as x= 12.3 and -8.6
So, taking the positive value of x= 12.3years.
Present ages:
Daughter's (x-3)years = 12.3-3 =9.30years (9 years 3 months)
Father's age: (4x-3)years= 4×12.3-3 = 46.21years (46 years 2 months 1 week)
Checking:
9.30×46.21= 429.753 = 430 (approximated