SOLUTION: father is four times as old as his son today. six years ago, the product of the numbers denoting their ages was 252.find their present ages

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: father is four times as old as his son today. six years ago, the product of the numbers denoting their ages was 252.find their present ages      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 943893: father is four times as old as his son today. six years ago, the product of the numbers denoting their ages was 252.find their present ages
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the son's age today
+4s+ = the father's age today
+s+-+6+ was the son's age 6 yrs ago
+4s+-+6+ was the father's age 6 yrs ago
------------------------------------
The product of the ages was:
+%28+s+-+6+%29%2A%28+4s+-+6+%29+=+252+
+4s%5E2+-+24s+-+6s+%2B+36+=+252+
+4s%5E2+-+30s+-+216+
+2s%5E2+-+15s+-+108+=+0+
use quadratic formula:
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-15+
+c+=+-108+
+s+=+%28+-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2+-+4%2A2%2A%28-108%29+%29%29+%2F+%282%2A2%29+
+s+=+%28+15+%2B-+sqrt%28+225+%2B+864%29%29+%2F+4+
+s+=+%28+15+%2B-+sqrt%28+1089%29%29+%2F+4+
+s+=+%28+15+%2B+33+%29+%2F+4+ ( take the positive square root )
+s+=+48%2F4+
+s+=+12+
and
+4s+=+4%2A12+
+4s+=+48+
The son is 12 and the father is 48
---------------
check:
+%28+s+-+6+%29%2A%28+4s+-+6+%29+=+252+
+%28+12+-+6+%29%2A%28+48+-+6+%29+=+252+
+6%2A42+=+252+
+252+=+252+
OK