Question 1121008: when the father was the same age as his daughter is now, she was 4 years old. when the daughter becomes the same age as her father is now, her father will be 79 years old. what are their ages
Found 4 solutions by Theo, Edwin McCravy, MathTherapy, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! good one.
let f = the father's age now.
let d = the daughter's age now.
not sure whether i needed to do it this way, but it worked.
when the father was the same age as his daughter is now, she was 4 years old.
let x equal the number of years when the father was the same age as his daughter is now.
the equations for that are:
f - x = d
d - x = 4
solve for x in the second equation to get:
x = d - 4
replace x with d - 4 in the first equation to get:
f - x = d becomes f - (d - 4) = d
simplify to get f - d + 4 = d
add d and subtract 4 from both sides of this equation to get:
f = 2d - 4 ***** hold on to this for later.
when the daughter becomes the same age as her father is now, her father will be 79 years old.
let y equal the number of years when the daughter is the same age as the father is now.
the equations for that are:
d + y = f
f + y = 79
solve for y in the second equation to get:
y = 79 - f
replace y in the first equation with that to get:
d + y = f becomes d + (79 - f) = f
simplify tto get d + 79 - f = f
add f to both sides 79 from both sides of this equation to get:
d = 2f - 79 ***** hold onto this for later.
later:
the equations you held are:
f = 2d - 4
d = 2f - 79
replace d with 2f - 79 in the first equation to get:
f = 2 * (2f - 79) - 4
simplify to get:
f = 4f - 158 - 4
combine like terms to get:
d = 4f - 162
add 162 and subtract d from both sides of this euation to get:
162 = 3f
solve for f to get:
f = 54
go back to f = 2d - 4 and replace f with 54 to get:
54 = 2d - 4
add 4 to both sides of this equation to get 58 = 2d
solve for d to get d = 58/2 = 29
d = 29
you now have f = 54 and d = 29
go back to f - x = d and replace f with 54 and d with 29
solve for x to get x = 54 - 29 = 25
25 years ago, the father was 54 - 25 = 29
25 years ago, the daughter was 29 - 25 = 4
your first 2 equations of:
f - x = d
d - x = 4
hold true when f = 54 and d = 29 and x = 25
54 - 25 = 29 which is the daughter's age now.
25 - 25 = 4 which is how old the daughter was when the father was her age.
go back to d + y = f and replace d with 29 and f = 54 to get:
29 + y = 54
solve for y to get y = 54 - 29 = 25
25 years from now, the daughter will be 29 + 25 = 54
29 years from now, the father will be 54 + 25 = 79
the second 2 equations of:
d + y = f
f + y = 79
hold true when d = 29 and f = 54 and y = 25
29 + 25 = 54 which is the age her father is now.
54 + 25 = 79 which is the age her father will be when she is as old as her father is now.
your solution is that the father is 54 and the daughter is 29.
25 years ago, he was 29 and she was 4.
25 years from now, he will be 79 and she will be 54.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! Let F = the Father's age
Let D = the Daughter's age
Let x = number of years the father is older than his daughter.
Thus F-x = D.
when the father was the same age as his daughter is now, she was 4 years old.
The father was the daughter's present age x years ago.
x years ago the daughter was D-x or 4, so D-x = 4
when the daughter becomes the same age as her father is now, her father will
be 79
She will become the father's age x years from now.
x years from now the father will be his present age plus x years, so F+x = 79.
We have three equations and three unknowns:
(1) F-x = D
(2) D-x = 4
(3) F+x = 79
Use (1) to substitute F-x for D in (2)
(F-x)-x = 4
F-x-x = 4
(4) F-2x = 4
Subtract equation (4) from equation (3)
(F+x)-(F-2x) = 79-4
F+x-F+2x = 75
3x = 75
x = 25
Substitute 25 for x in (2)
(2) D-x = 4
D-25 = 4
D = 29
Substitute 25 for x in (3)
(3) F+x = 79
F+25 = 79
F = 54
So the Father is 54 and the daughter is 29.
Edwin
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
when the father was the same age as his daughter is now, she was 4 years old. when the daughter becomes the same age as her father is now, her father will be 79 years old. what are their ages
Let the daughter’s and father’s ages be D, and F, respectively
Then difference in ages = F – D
We then see that: D – (F – D) = 4_____D – F + D = 4____2D – F = 4_____F = 2D – 4 ---- eq (i)
Also, we see that F + (F – D) = 79_____2F – D = 79 ----- eq (ii)
2(2D – 4) – D = 79 ------- Substituting 2D – 4 for F in eq (ii)
4D – 8 – D = 79
4D – D = 79 + 8
3D = 87
D, or daughter is: 
Father’s age: 
Answer by ikleyn(52788)  (Show Source):
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