SOLUTION: 3 YEARS AGO THE RATIO OF THE AGE OF A FATHER AND HIS DAUGHTER WAS 4:1. AFTER 5 YEARS THE RATIO WILL BE 8:3. FIND THEIR PRESENT AGES.

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Question 608465: 3 YEARS AGO THE RATIO OF THE AGE OF A FATHER AND HIS DAUGHTER WAS 4:1. AFTER 5 YEARS THE RATIO WILL BE 8:3. FIND THEIR PRESENT AGES.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
3 YEARS AGO THE RATIO OF THE AGE OF A FATHER AND HIS DAUGHTER
WAS 4:1. AFTER 5 YEARS THE RATIO WILL BE 8:3. FIND THEIR PRESENT
AGES.
(F-3):(D-3) = 4:1

(F+5):(D+5) = 8:3

The system of equations is


Cross-multiply both equations:



Distribute:





Solve by substitution.

Solve the first equation for F

F = 4D - 9

Substitute (4D - 9) for F in the second
equation:

3(4D - 9) - 8D = 25
 12D - 27 - 8D = 25
            4D = 52
             D = 13

Substitute (13) for D in

F = 4D - 9
F = 4(13) - 9
F = 52 - 9
F = 43.

The father is 43 and the daughter is 13.

Checking with the words:

3 YEARS AGO THE RATIO OF THE AGE OF A FATHER was 
43-3 or 40 AND HIS DAUGHTER WAS 13-3 or 10 and 
40:10 is in the ratio of 4:1 (dividing 40 and 10 
both by 10).

AFTER 5 YEARS THE father will be 43+5 or 48 and 
the daughter will be 13+5 or 18 and 48:18 is in 
the ratio of  8:3 (dividing 48 and 18 both by 6).

Edwin
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