SOLUTION: The sum of two numbers is sixty-five, and if the larger number is divided by the smaller number, then quotient is three and the remainder is five. Find the numbers.

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Question 121044: The sum of two numbers is sixty-five, and if the larger number is divided by the smaller number, then quotient is three and the remainder is five. Find the numbers.
Answer by solver91311(24713) About Me  (Show Source):
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Let's say your numbers are m and n.

The first thing we know is that n+%2B+m+=+65.

Let's assume that n%3Em, so n%2Fm=3%2B5%2Fm

Multiplying by m:

n=3m+%2B+5, or
n-3m=5

Now we have two standard form equations in two variables, so

n+%2B+m+=+65
n-3m=5

Multiply the second equation by -1:

n+%2B+m+=+65
-n%2B3m=-5

Now add the equations, term by term:

0n%2B4m=60

Divide by 4:

m=15

Now that we know the value of m, we can calculate n by n=65-15=50

Note that n%3Em is true.

Check:
50 divided by 15 is 3 with a remainder of 5. Checks.