Genevieve is buying a car audio system that consists of a stereo, speakers, and amplifiers. She is choosing between 5 types of stereos and 2 types of amplifiers. If she has a total of 30 choices, how many types of speakers must there be?

3
6
10
20

1 answer

To determine the number of types of speakers Genevieve can choose from, let’s denote the number of types of speakers as \( S \).

Genevieve has 5 types of stereos and 2 types of amplifiers. The total number of combinations she can create with these components is given by the formula:

\[ \text{Total Choices} = (\text{Number of Stereos}) \times (\text{Number of Amplifiers}) \times (\text{Number of Speakers}) \]

Plugging in the values we have:

\[ 30 = 5 \times 2 \times S \]

This simplifies to:

\[ 30 = 10S \]

To find \( S \), divide both sides by 10:

\[ S = \frac{30}{10} = 3 \]

Thus, the number of types of speakers must be \( \boxed{3} \).