Product =6050, quotient =1/2. Find 2 numbers

1 answer

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 \( y \).

  1. From the product: \[ x \cdot y = 6050 \]

  2. 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.