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 Adele is buying a sport utility vehicle. She is trying to choose among a variety of options.

Brand: Brand A or Brand B

Transmission: 4-speed standard, 5-speed standard, or automatic

Bumper: steel, vinyl, or 2x4 boards

Roof: hard top or convertible top

Adele calculates that she has 2 + 3 + 3 + 2, or a total of 10, possible vehicle choices

What is Adele’s error?
She should have added only the transmission and bumper choices.
She should have added only the brand and roof choices.
She should have multiplied the total of all the choices.
She should have multiplied only the brand and roof choices.
as 36 different choices, how many kinds of amplifiers must there be?

a) Option 3 - She should have multiplied the total of all the choices.

b) The total number of amplifiers is 3

Step-by-step explanation:

Step 1 :                      

Given,

Number of models of stereos Antonio can select from  = 4

Number of styles of speakers Antonio can select from = 3

Number of brands available for Adele = 2

Number of Transmission available for Adele = 3

Number of bumpers available for Adele = 3

Number of roofs available for Adele = 2

Step 2:

a)

From Step 1 , we can see that the total number of possible choices of vehicles  Adele has  = 2 × 3 × 3 × 2 = 36

Total possible choices as calculated by Adele = 2 + 3 + 3 + 2 = 10

Hence we can see that the error is that Adele has added the total possible choices instead of multiplying them.

So her error is as specified in option 3 - She should have multiplied the total of all the choices.

Step 4 :

b)

Given number of total available choices = 36

We need to find the number of amplifiers. Let x be the number of amplifiers.

As we know from step 1 the total available choices for Antonio are

4 × 3 × x = 36

=>12 x = 36

=> x =   = 3

Hence the total number of amplifiers is 3

Step 5 :

Answer :

a) Option 3 - She should have multiplied the total of all the choices.

b) The total number of amplifiers is 3

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step-by-step explanation:

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