SOLUTION: Mum is 4 times older than her daughter. In 4 years time she will be 3 times older than her daughter. In how many years will mum be exactly twice her daughters age? What will their

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Question 1034779: Mum is 4 times older than her daughter. In 4 years time she will be 3 times older than her daughter. In how many years will mum be exactly twice her daughters age? What will their ages be?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Mum's age now
Let +d+ = daughter's age now
---------------------------
(1) +m+=+4d+
(2) +m+%2B+4++=+3%2A%28+d+%2B+4+%29+
-------------------------
Substitute (1) into (2)
(2) +4d+%2B+4++=+3%2A%28+d+%2B+4+%29+
(2) +4d+%2B+4+=+3d+%2B+12+
(2) +d+=+8+
and
(1) +m+=+4d+
(1) +m+=+4%2A8+
(1) +m+=+32+
--------------------
Let +x+ = the number of years from now
when Mum's age is twice daughter's age
--------------------
(3) +m+%2B+x++=+2%2A%28+d+%2B+x+%29+
(3) +32+%2B+x++=+2%2A%28+8+%2B+x+%29+
(3) +32+%2B+x+=+16+%2B+2x+
(3) +x+=+16+
In 16 years Mum will be twice daughter's age
--------------------
check:
+32+%2B+16+=+48+
and
+8+%2B+16+=+24+
48 is twice 24
OK