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.

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) (Show Source): You can put this solution on YOUR website!
Let's say your numbers are m and n.

The first thing we know is that .

Let's assume that , so

Multiplying by m:

, or

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

Multiply the second equation by -1:

Now add the equations, term by term:

Divide by 4:

Now that we know the value of m, we can calculate n by

Note that is true.

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