SOLUTION: Louis is 3 times as old as Mackenzie.In 8 years their ages will be 100.How old are they now? Answer with steps please!!

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Question 726059: Louis is 3 times as old as Mackenzie.In 8 years their ages will be 100.How old are they now?
Answer with steps please!!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Louis's age now
Let +b+ = Mackenzie's age now
+a+%2B+8+ = Louis's age in 8 years
+b+%2B+8+= Mackenzie's age in 8 years
given:
(1) +a+=+3b+
(2) +a+%2B+8+%2B+b+%2B+8+=+100+
-------------------------
(2) +a+%2B+b+%2B+16+=+100+
(2) +a+%2B+b+=+84+
Substitute (1) into (2)
(2) +3b+%2B+b+=+84+
(2) +4b+=+84+
(2) +b+=+21+
and, since
(1) +a+=+3b+
(1) +a+=+3%2A21+
(1) +a+=+63+
Louis is 63 and Mackenzie is 21
check:
(2) +a+%2B+b+%2B+16+=+100+
(2) +63+%2B+21+%2B+16+=+100+
(2) +100+=+100+
OK