SOLUTION: beths mom is 6 times older than beth. beths dad is 7 years older than beths mom the sum of their ages is 72 how old are each of them

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Question 462374: beths mom is 6 times older than beth. beths dad is 7 years older than beths mom the sum of their ages is 72 how old are each of them
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Beth's Mom's age now
Let +b+ = Beth's age now
Let +d+ = Beth's Dad's age now
given:
(1) +m+=+6b+
(2) +d+=+m+%2B+7+
(3) +m+%2B+b+%2B+d+=+72+
This is 3 equations abnd 3 unknowns,
so it's solvable
From (1):
(1) +b+=+m%2F6+
Substitute (1) and (2) into (3)
(3) +m+%2B+m%2F6+%2B+m+%2B+7+=+72+
(3) +2m+%2B+m%2F6+=+72+-+7+
(3) +%2813%2F6%29%2Am+=+65+
(3) +m+=+%286%2A65%29%2F13+
(3) +m+=+30+
and,
(1) +b+=+m%2F6+
(1) +b+=+30%2F6+
(1) +b+=+5+
and,
(2) +d+=+m+%2B+7+
(2) +d+=+37+
30 = Beth's Mom's age now
5 = Beth's age now
37 = Beth's Dad's age now