SOLUTION: Jenny is 5 years older than her brother. 4 years ago the product of their ages was the same as 37 more than Jenny's present age subtracted from the square of the brother's present

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Question 612339: Jenny is 5 years older than her brother. 4 years ago the product of their ages was the same as 37 more than Jenny's present age subtracted from the square of the brother's present age.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Jenny's age now
Let +b+ = Brother's age now
Given:
(1) +j+=+b+%2B+5+
(2) +%28+j+-+4+%29%2A%28+b+-+4+%29+=+b%5E2+-+%28+j+%2B+37+%29+
(2) +j%2Ab+-+4b+-+4j+%2B+16+=+b%5E2+-+j+-+37+
(2) +j%2Ab+-+4b+%2B+16+=+b%5E2+%2B+3j+-+37+
(2) +j%2Ab+%2B+16+=+b%5E2+%2B+4b+%2B+3j+-+37+
(2) +j%2Ab+%2B+53+=+b%5E2+%2B+4b+%2B+3j+
Substitute (1) into (2)
(2) +%28+b+%2B+5+%29%2Ab+%2B+53+=+b%5E2+%2B+4b+%2B+3%2A%28+b+%2B+5+%29+
(2) +b%5E2+%2B+5b+%2B+53+=+b%5E2+%2B+4b+%2B+3b+%2B+15+
(2) +7b+-+5b+=+53+-+15+
(2) +2b+=+38+
(2) +b+=+19+
and, since
(1) +j+=+b+%2B+5+
(1) +j+=+19+%2B+5+
(1) +j+=+24+
Jenny is 24 and her Brother is 19
check:
(2) +%28+j+-+4+%29%2A%28+b+-+4+%29+=+b%5E2+-+%28+j+%2B+37+%29+
(2) +%28+24+-+4+%29%2A%28+19+-+4+%29+=+19%5E2+-+%28+24+%2B+37+%29+
(2) +20%2A15+=+361+-+61+
(2) +300+=+300+
OK