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.

Algebra ->  Equations -> 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.      Log On


   

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) About Me  (Show Source):
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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
system%28%28F-3%29%2F%28D-3%29+=+4%2F1%2C%0D%0A%28F%2B5%29%2F%28D%2B5%29+=+8%2F3%29

Cross-multiply both equations:

system%28F-3+=+4%28D-3%29%2C%0D%0A3%28F%2B5%29+=+8%28D%2B5%29%29

Distribute:

system%28F-3+=+4D+-+12%2C%0D%0A3F+%2B+15+=+8D+%2B+40%29

system%28F-4D=+-9%2C%0D%0A3F-8D+=+25%29

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