Problem Solving

Most of the Age problems I have seen STATE the number of years in the future or past that one of the people should be "a certain age". For example, "In 15 years, John will be 3 times Pauls age" or "7 years ago, Paul would be..." How do you handle the case where you are solving for the number of years? See problem below:

Katie was 24 years old when her daughter Heidi was born. In how many years will Katie be four years less that five times her daughter's age?

[spoiler]Answer: 7[/spoiler][spoiler]

I tried setting it up this way:

Today - Katie = 24
Today - Heidi = 0

Some time in the future - Katie = 5(x-4)
Some time in the future - Heidi = x

How would the equation be set up to incorporate the unknown future number of years? Are we solving for two variables here?

let x be the number of years in the future as well as the age of her daughter at that time (since she is 0 when she is born)

(24+x) + 4 = 5x (ie in x years, mother will be 4 years less than 5 times daughters age)

28 = 4x

x = 7

So you mean

Katies age now: 24 plus
Years in the future: x

Will be equal to:

5x-4 (x = daughters age)

So to add a twist. If we used the same problem only when Katie was 24, her daughter not just born but was 2 years old - the equation would be:

24 + x = 5(2+x)-4?

katies age (present)=K=24
Heide's age (present)=H=0

say, y years later :Katie be four years less that five times Heide's age
(K+y)+4=5(H+y)......(1)
now H=0,K=24
24+y+4=5y
4y=24+4, we get y=28/4=7

now if Heide was 2yrs when Katie was 24yrs, we get
H=2,K=24
(24+y)+4=5(2+y)..wud give y=4 1/2 yrs

hope this helps

I like to solve these problems methodically
Now
k = 24
d = 0

x years into the future we add x to each of their ages
k+x = 5 (d + x) - 4
k + x = 5d + 5x - 4 [substitute k = 24 d =0]
24 + x = 5x - 4 [add 4 to both sides]
28 + x = 5x [subtract x from both sides]
28 = 4x
x =7