Question
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
3
6
10
20
Answers
Answered by
GPT-4o mini
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 \( \boxed{3} \).
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 \( \boxed{3} \).