Maths Help?

Question

A father is 5 more than his sons age squared. In 20 years the father is twice his sons age. How old is the father?

How do i solve is systematically using quadratics?

Answer 1

Let the son be x years and the father y. We get
y = 5 + x^2
y + 20 = 2 (x + 20)
So y = 2x + 20, put this into the first equation to get
2x + 20 = 5 + x^2
<=> x^2 - 2x - 15 = 0
<=> (x - 5) (x + 3) = 0
So x is 5 or -3, but -3 is impossible, so x = 5 and y = 5 + 5^2 = 30. So the son is 5 and the father is 30.

Answer 2

son's age now = x
father's age now = y
father's age now, using relationship to son's age =
son's age in 20 years = (x + 20)
father's age in 20 years = y+ 20
father's age in 20 years, using relationship to son's age =
Using quadratics just means that your equation will have an x^2 (x squared) in it, and that term comes from the first given statement.

Now make an equation using the two expressions for the father's age, since they are equal.

You will need to then add and subtract and combine terms until you reach a factorable equation (x^2 -bx - c =0)

If you do everything right, you will find that the son is 5 and the father is 25 -- but remember, understanding how to do the problem is FAR more important than getting the answer. That's why I'm explaining how but not giving you the expressions and equations.

I'll check back to see how quickly you figured it out.

Answer 3

x is son's age now
x^2 + 5 is father's age now

x + 20 is son's age in 20 years
x^2 + 5 + 20 or x^2 + 25 is father's age in 20 years
2(x+20) = x^2 + 25
2x + 40 = x^2 + 25
set everything = to zero
x^2 -2x - 15 = 0
factor
(x -5) (x + 3) = 0
x = 5 or x = -3, but ages cannot be negative so discard x = -3.
the son is 5 now and the father is x^2 + 5 or 5^2 + 5 or 25 + 5 or 30.

Answer 4

x = y2(squared) + 5 ...(1)

x+20 = (y+20)2
x+20=2y+40
x=2y+20...(2)

substitute (2) into (1)

y2(squared) + 5 = x
y2(squared) + 5 =2y + 20
y2(squared) = 2y +15
y2(squared) -2y - 15 =0
(y-5)(y+3)=0
y=5 @ y= -3

x= y2(squared) + 5
x= (5)2(squared) + 5
x = 30

Answer 5

hey i already posted a picture of ur question with a worked solution at http://www.icedor.com under Elementary Maths Forum under Algebraic Manipulation. the answer i gave is labeled.. quadratics using worded problems. i cant post a picture here... u might want to check out the solution at that site.. they allow posting of pictures.. easier to simply write the solution out using a write pad or scan a picture..
http://www.icedor.com/icedoronline/course/index.php?cid=FLM101

Answer 6

i have no idea.
im sooo sorry