SOLUTION: Mary is now four times as her daughter.four years ago the product of their ages was 40 find their present ages. Thankyou

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Question 638254: Mary is now four times as her daughter.four years ago the product of their ages was 40 find their present ages. Thankyou
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Mary's age now
Let +d+ = Daughter's age now
given:
(1) +m+=+4d+
(2) +%28+m+-+4+%29%2A%28+d+-+4+%29+=+40+
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Substitute (1) into (2)
(2) +%28+4d+-+4+%29%2A%28+d+-+4+%29+=+40+
(2) +4%2A+%28+d+-+1+%29%2A%28+d+-+4+%29+=+40+
(2) ++%28+d+-+1+%29%2A%28+d+-+4+%29+=+10+
(2) +d%5E2+-d+-+4d+%2B+4+=+10+
(2) +d%5E2+-+5d+-+6+=+0+
(2) +%28+d+-+6+%29%2A%28+d+%2B+1+%29+=+0+
+d+=+6+
+d+=+-1+
Daughter's age must be positive, so
the Daughter is 6
and, since
(1) +m+=+4d+
(1) +m+=+4%2A6+
(1) +m+=+24+
The Mother is 24
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check answers
(2) +%28+m+-+4+%29%2A%28+d+-+4+%29+=+40+
(2) +%28+24+-+4+%29%2A%28+6+-+4+%29+=+40+
(2) +20%2A2+=+40+
(2) +40+=+40+
OK