SOLUTION: A man is five times as old as his daughter. six years ago,the product of their age was 324.find their present age.

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Question 556152: A man is five times as old as his daughter. six years ago,the product of their age was 324.find their present age.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = man's age now
Let +d+ = Daughter's age now
given:
(1) +m+=+5d+
(2) +%28+m+-+6+%29%2A%28+d+-+6+%29+=+324+
-----------------
Substitute (1) into (2)
(2) +%28+5d+-+6+%29%2A%28+d+-+6+%29+=+324+
(2) +5d%5E2+-+6d+-+30d+%2B+36+=+324+
(2) +5d%5E2+-+36d+-+288+=+0+
Use quadratic formula
d+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+5+
+b+=+-36+
+c+=+-288+
+d+=+%28-%28-36%29+%2B-+sqrt%28+%28-36%29%5E2-4%2A5%2A%28-288%29+%29%29%2F%282%2A5%29+
+d+=+%28+36+%2B-+sqrt%28+1296+%2B+5760+%29%29%2F+10+
+d+=+%28+36+%2B-+sqrt%28+7056+%29%29%2F+10+
+d+=+%28+36+%2B-+84+%29%2F+10+
+d+=+%28+36+%2B+84+%29+%2F+10+
+d+=+120%2F10+
+d+=+12+
and,
(1) +m+=+5d+
(1) +m+=+5%2A12+
(1) +m+=+60+
The man is 60 and the daughter is 12
check:
(2) +%28+m+-+6+%29%2A%28+d+-+6+%29+=+324+
(2) +%28+60+-+6+%29%2A%28+12+-+6+%29+=+324+
(2) +54%2A6+=+324+
(2) +324+=+324+
OK