SOLUTION: The ratio of the age of a father and his son two years ago was 10:1. Four years hence the age of the father will be 4 times the age of his son. what is the difference in the age of

Algebra ->  Proportions  -> Lessons -> SOLUTION: The ratio of the age of a father and his son two years ago was 10:1. Four years hence the age of the father will be 4 times the age of his son. what is the difference in the age of      Log On


   



Question 1111128: The ratio of the age of a father and his son two years ago was 10:1. Four years hence the age of the father will be 4 times the age of his son. what is the difference in the age of the father and son?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = father's age now
Let +b+ = son's age now
----------------------------------
(1) +%28+a+-+2+%29+%2F+%28+b+-+2+%29+=+10%2F1+
(2) +a+%2B+4+=+4%2A%28+b+%2B+4+%29+
----------------------------------
(1) +a+-+2+=+10%2A%28+b+-+2+%29+
(1) +a+-+2+=+10b+-+20+
(1) +-a+%2B+10b+=+18+
and
(2) +a+%2B+4+=+4b+%2B+16+
(2) +a+-+4b+=+12+
-------------------------------
Add (1) and (2)
(1) +-a+%2B+10b+=+18+
(2) +a+-+4b+=+12+
----------------------------
+6b+=+30+
+b+=+5+
and
(2) +a+-+4b+=+12+
(2) +a+-+4%2A5+=+12+
(2) +a+=+12+%2B+20+
(2) +a+=+32+
-----------------------------
+a+-+b+=+32+-+5+
+a+-+b+=+27+
The difference in their ages is 27
-------------------------------------
check:
(1) +%28+a+-+2+%29+%2F+%28+b+-+2+%29+=+10+
(1) +%28+32+-+2+%29+%2F+%28+5+-+2+%29+=+10+
(1) +30+%2F+3+=+10+
(1) +10+=+10+
and
(2) +a+%2B+4+=+4%2A%28+b+%2B+4+%29+
(2) +32+%2B+4+=+4%2A%28+5+%2B+4+%29+
(2) +36+=+4%2A9+
(2) +36+=+36+
OK