SOLUTION: Divide 32 into two parts such that if the larger is divided by the smaller, the quotient is 2 and the remainder is 5.

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Question 459212: Divide 32 into two parts such that if the larger is divided by the smaller, the quotient is 2 and the remainder is 5.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the parts = a and b,
with a being larger
given:
(1) +a+%2B+b+=+32+
(2) +a%2Fb+=+2+%2B+5%2Fb+
Multiply both sides by b
(2) +a+=+2b+%2B+5+
Substitute (1) into (2)
(2) +32+-+b+=+2b+%2B+5+
(2) +3b+=+32+-+5+
(2) +3b+=+27+
(2) +b+=+9+
and
(1) +a+%2B+b+=+32+
(1) +a+%2B+9+=+32+
(1) +a+=+23+
check answers:
(2) +a%2Fb+=+2+%2B+5%2Fb+
(2) +23%2F9+=+2+%2B+5%2F9+
(2) +23+=+18+%2B+5+
(2) +23+=+23+
OK