Question

Jack and Jim sign up with an online music store. Jack chooses 15 downloads for $19.75, and Jim chooses 40 downloads for $43.50. Both amounts include a one-time registration fee, which is the same for each account, plus the fee for the number of downloads. What is the registration fee, and what is the cost of each download?

A. The registration fee is $5.50, and the cost per download is $0.95.

B. The registration fee is $3.50, and the cost per download is $1.00.

C. The registration fee is $2.50, and the cost per download is $0.85.

D. The registration fee is $4.75, and the cost per download is $1.00.

Answer 1

Thus, the correct answer is option A

Explanation-

Let the cost of each n load be "x" while the one time registration fee be "y"

Jack chooses
`15\\` downloads and the total expenditure of him including tex]15\\[/tex] downloads and one time registration fee "y" is $
`19.75 \\`

This can be represented as

Expenditure by Jack
`= y + (15 * x)\\`

`19.75 = y + (15 * x)\\`...................Eq (A)

Similarly , Jim chooses
`40\\` downloads and the total expenditure of him including tex]40\\[/tex] downloads and one time registration fee "y" is $
`43.50 \\`.

This can be represented as

Expenditure by Jim
`= y + (40 * x)\\`

`43.50 = y + (40 * x)\\`...................Eq (B)

From equation A we get

`y = 19.75 - (15 * x) \\`

Substituting this values of y in equation (B) ,we get
`43.50 = {19.75 - (15 *x)} + (40 * x)\\43.50 - 19.75 = 40x - 15 x\\23.75 = 25x\\x = 0.95`

Substituting this value of x in equation A, we get

`y = 19.75 - (15 * x)\\y = 19.75 - (15 * 0.95) \\y =  5.5\\`

Thus, the correct answer is option A

Answer 2

Let us assume the one time registration fee = y dollars
Let us assume the cost of each download = x dollars
Then
15x + y = 19.75
y = 19.75 - 15x
Let us put the value of y from the first equation in the second equation,
Then
40x + y = 43.50
40x -15x + 19.75 = 43.50
25x = 43.50 - 19.75
25x = 23.75
x = 23.75/25
= 0.95 dollars
Putting the value of x in the first equation, we get
15x + y = 19.75
(15 * 0.95) + y = 19.75
14.25 + y = 19.75
y = 5.50 dollars
From the above deductions we can conclude that the correct option among all the options that are given in the question is option "A".