Question

Music Company A charges a $15 membership fee and $0.75 each to download a song. Music Company B charges $0.90 each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.

Answer 1

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

Linear Equation:

The mathematical expressions that we used to find unknown numbers are called Linear Equations. These can be formed by variables and constant terms according to given conditions. Here we use variables like x, y, z, etc to represent unknown variables.

 

Here we have,

Music company A charges a $ 15 membership fee and a $ 0.75 for each downloaded song

Music company B charges $ 0.90 for each downloaded song without the membership fee

Given question

a. For what number of songs will both companies charge the same amount?  

Let for x songs both companies will charge the same amount

Cost to download x songs from Company A

=> 15 + 0.75x

Cost to download x songs from Company B

=>  0.90x

As we assumed both costs are the same

=> 15 + 0.75x = 0.90x

=> 0.90x - 0.75 = 15

=> 0.15x = 15

-> x = 100

Therefore,

The number of songs that both companies will charge the same amount is 100.

b) You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money?  

Cost of 150 that charges company A =  15 + 150(0.75)  

= 15 + 150(0.75)  = 15 + 112.5 = 127.5  

Therefore,

Company A will charge $ 127.5 for 150 songs

Cost of 150 songs that charges company B = 150(0.90)

= $ 135  

Company B will charge $ 135 for 150 songs

Therefore,

Company B will charge $ 135 for 150 songs

Thus,

To pay the least amount of money we need to choose Company B.

Therefore,

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

Learn more about Linear Equations at

brainly.com/question/11897796

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