Gary and Elena have a talk show on TV. Gary has been on 325 episodes of the show, and Elena has been on 525 episodes. What is the ratio of episodes with Gary to episodes with Elena?

Question

A.
21 to 13
B.
34 to 13
C.
13 to 34
D.
13 to 21

Answer 1

To find the ratio of episodes with Gary to episodes with Elena, we need to write it as a fraction and simplify it:

The ratio is:

\[ \text{Ratio} = \frac{\text{Episodes with Gary}}{\text{Episodes with Elena}} = \frac{325}{525} \]

Now we can simplify this fraction. We can find the greatest common divisor (GCD) of 325 and 525 first.

The prime factorizations are:

• \( 325 = 5^2 \times 13 \)
• \( 525 = 5^2 \times 21 = 5^2 \times 3 \times 7 \)

The common factor is \( 5^2 \), so the GCD is 25.

Now, we can simplify:

\[ \frac{325 \div 25}{525 \div 25} = \frac{13}{21} \]

Thus, the simplified ratio of episodes with Gary to episodes with Elena is:

\[ \text{Ratio} = 13 : 21 \]

So the correct answer is D. 13 to 21.