SOLUTION: The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 and the remainder is 1. Find the numbers.

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Question 437284: The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 and the remainder is 1. Find the numbers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the larger number = a
Let the smaller number = b
given:
(1) a+%2B+b+=+17+
(2) +a%2Fb+=+3+%2B+1%2Fb+
----------------
Multiply both sides of (2) by b
(2) +a+=+3b+%2B+1+
Substitute this into (1)
(1) +3b+%2B+1+%2B+b+=+17+
(1) +4b+=+16+
+b+=+4+
and
(1) a+%2B+b+=+17+
+a+=+13+
The numbers are 4 and 13