SOLUTION: the ratio of ages of mother and daughter is 7:20. 4 years ago mothers age was 6 times that of her daughter. what is the present age of the mother

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Question 625355: the ratio of ages of mother and daughter is 7:20. 4 years ago mothers age was 6 times that of her daughter. what is the present age of the mother
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Mother's age now
Let +d+ = daughter's age now
given:
(1) +d%2Fm+=+7%2F20+
(2) +m+-+4+=+6%2A%28+d+-+4+%29+
---------------------
(1) +20d+=+7m+
(1) +m+=+%2820%2F7%29%2Ad+
Substitute (1) into (2)
(2) +%2820%2F7%29%2Ad+-+4+=+6%2A%28+d+-+4+%29+
Multiply both sides by +7+
(2) +20d+-+28+=+42%2A%28+d+-+4+%29+
(2) +20d+-+28+=+42d+-+168+%29+
(2) +22d+=+168+-+28+
(2) +22d+=+140+
(2) +d+=+70%2F11+
and, since
(1) +m+=+%2820%2F7%29%2Ad+
(1) +m+=+%2820%2F7%29%2A%2870%2F11%29+
(1) +m+=+18.2+
The Mother is 18. Check my math- these types of
problems usually have whole number answers.
check answer:
(2) +m+-+4+=+6%2A%28+d+-+4+%29+
(2) +200%2F11+-+4+=+6%2A%28+70%2F11+-+4+%29+
Multiply both sides by +11+
(2) +200+-+44+=+420+-+264+
(2) +156+=+156+
It checks