If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.

Explanation

To solve the problem, we will define the two numbers and set up equations based on the information provided.

Let:
- \( x \) = larger number
- \( y \) = smaller number

### Step 1: Set up the first equation
According to the first statement, if three times the larger number is divided by the smaller number, we get a quotient of 4 and a remainder of 3.
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