SOLUTION: Amother is three times as old as her child seven years ago the products of their ages was 104 find the present age of the child?

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Question 872376: Amother is three times as old as her child seven years ago the products of their ages was 104 find the present age of the child?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = the mother's age now
Let +p+ = the child's age now
------------------------------
(1) +m+=+3p+
(2) +%28+m+-+7+%29%2A%28+p+-+7+%29+=+104+
-----------------------------
(2) +m%2Ap+-+7p+-+7m+%2B+49+=+104+
(2) +m%2Ap+-+7%2A%28+p+%2B+m+%29+=+104+-+49+
(2) +m%2Ap+-+7%2A%28+p+%2B+m+%29+=+55+
Substitute (1) into (2)
(2) +3p%2Ap+-+7%2A%28+p+%2B+3p+%29+=+55+
(2) +3p%5E2+-+28p+-+55+=+0+
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Solve using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-28+
+c+=+-55+
+p+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2-4%2A3%2A%28-55%29+%29%29%2F%282%2A3%29+
+p+=+%28+28+%2B-+sqrt%28+784+%2B+660+%29%29%2F6+
+p+=+%28+28+%2B-+sqrt%28+1444+%29%29%2F6+
+p+=+%28+28+%2B+38%29%2F6+ ( can't use the negative square root )
+p+=++66%2F6+
+p+=+11+
--------------
(1) +m+=+3p+
(1) +m+=+3%2A11+
(1) +m+=+33+
The mother is 33 and the child is 11
check:
(2) +%28+m+-+7+%29%2A%28+p+-+7+%29+=+104+
(2) +%28+33+-+7+%29%2A%28+11+-+7+%29+=+104+
(2) +26%2A4+=+104+
(2) +104+=+104+
OK