Let's denote the two unknown numbers as \(x\) and \(y\), with \(x\) being the larger number.
According to the information given:
1. The quotient of the two numbers is 5.
This can be written as the equation: \( \frac{x}{y} = 5 \)
2. The sum of the two numbers is 12.
This can be written as the equation: \( x + y = 12 \)
Now let's solve these equations step by step.
From equation (1), we can isolate \(x\):
\( \frac{x}{y} = 5 \)
\( x = 5y \)
Now, we'll substitute \(x\) in equation (2) with \(5y\):
\( 5y + y = 12 \)
\( 6y = 12 \)
\( y = \frac{12}{6} \)
\( y = 2 \)
Now that we have the value for \(y\), we can find \(x\) using the equation \( x = 5y \):
\( x = 5 \cdot 2 \)
\( x = 10 \)
So, the two numbers are \(x = 10\) and \(y = 2\).
