SOLUTION: Dave is 6 years older than Debbie and Joan is three times Debbie's age. Eight years from now, the sum of Debbie's and Joan's age will be five times Dave's age four years ago. How o

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Question 1013873: Dave is 6 years older than Debbie and Joan is three times Debbie's age. Eight years from now, the sum of Debbie's and Joan's age will be five times Dave's age four years ago. How old is each?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Dave's age now
Let +b+ = Debbie's age now
Let +c+ = Joan's age now
-------------------------
given:
(1) +a+=+b+%2B+6+
(2) +c+=+3b+
(3) +%28+b+%2B+8+%29+%2B+%28+c+%2B+8+%29+=+5%2A%28+a+-+4+%29+
---------------------------------
(3) +b+%2B+c+%2B+16+=+5a+-+20+
(3) +5a+-+b+-+c+=+36+
Substitute (1) and (2) into (3)
(3) +5%2A%28+b+%2B+6+%29+-+b+-+3b+=+36+
(3) +5b+%2B+30+-+b+-+3b+=+36+
(3) +b+=+6+
and
(1) +a+=+b+%2B+6+
(1) +a+=+6+%2B+6+
(1) +a+=+12+
and
(2) +c+=+3b+
(2) +c+=+3%2A6+
(2) +c+=+18+
--------------------
Dave is 12
Debbie is 6
Joan is 18
------------
check:
(3) +%28+b+%2B+8+%29+%2B+%28+c+%2B+8+%29+=+5%2A%28+a+-+4+%29+
(3) +%286+%2B+8+%29+%2B+%28+18+%2B+8+%29+=+5%2A%28+12+-+4+%29+
(3) +14+%2B+26+=+5%2A8+
(3) +40+=+40+
OK
(2) +c+=+3b+
(2) +18+=+3%2A6+
(2) +18+=+18+
OK
(1) +a+=+b+%2B+6+
(1) +12+=6+%2B+6+
(1) +12+=+12+
OK