To find two numbers whose product is 6050 and whose quotient is \( \frac{1}{2} \), we can set up the following equations based on the information given:
Let the two numbers be \( x \) and \( y \).
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From the product: \[ x \cdot y = 6050 \]
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From the quotient: \[ \frac{x}{y} = \frac{1}{2} \implies x = \frac{1}{2}y \]
Now, substitute the expression for \( x \) from the second equation into the first equation:
\[ \frac{1}{2} y \cdot y = 6050 \]
This simplifies to:
\[ \frac{1}{2} y^2 = 6050 \]
Multiply both sides by 2 to eliminate the fraction:
\[ y^2 = 12100 \]
Now, take the square root of both sides:
\[ y = \sqrt{12100} = 110 \]
Now that we have \( y = 110 \), we can find \( x \):
\[ x = \frac{1}{2}y = \frac{1}{2} \cdot 110 = 55 \]
So the two numbers are:
\[ x = 55 \quad \text{and} \quad y = 110 \]
Thus, the two numbers are 55 and 110.