Question

antonio is buying a stereo, speakers, and amplifiers for his car audio system. he is choosing among 4 models of stereos and 3 styles of speakers. if he has 36 different choices, how many kinds of amplifiers must there be? options: 2, 3, 4, 12

Explanation:

Step1: Recall the multiplication principle

The total number of choices is the product of the number of choices for each component. Let the number of amplifier kinds be \( x \). We know the number of stereo models is 4, speaker styles is 3, and total choices is 36. So the formula is \( 4\times3\times x = 36 \).

Step2: Simplify the left - hand side

First, calculate \( 4\times3 = 12 \). So the equation becomes \( 12x=36 \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 12x = 36 \) by 12. \( x=\frac{36}{12}=3 \).

Answer:

3