Question

Music store is having a clearance sale on all of its vinyl records, CDs, and electronic downloads. For the sale, each item (vinyl, CD, and electronic download) costs the same regardless of the artist, with the price including the tax. Sarah, Jamie, and Frank decide to make the most of this sale, and they each purchase several items. Sarah buys 3 vinyl records, 4 CDs, and 1 electronic download for a total of $32. Jamie buys 2 vinyl records, 5 CDs, and 7 electronic downloads for a total of $37. Frank buys 6 CDs, and 6 electronic downloads for a total of $30. What is the price of each vinyl, CD, and electronic download?
A. $5 for each vinyl, $1 for each CD, and $4 for each electronic download
B. $5 for each vinyl, $4 for each CD, and $1 for each electronic download
C. $4 for each vinyl, $5 for each CD, and $1 for each electronic download
D. $1 for each vinyl, $4 for each CD, and $5 for each electronic download

Answer 1

Answer:

• B. $5 for each vinyl, $4 for each CD, and $1 for each electronic download

Step-by-step explanation:

Let the prices be

• Vinyl - x
• CD - y
• Electronic download - z

Set the following equations based on the number of purchased items

Sarah

• 3x + 4y + z = 32

Jamie

• 2x + 5y + 7z = 37

Frank

• 6x + 6z = 36 (note: it can't be 30, corrected in the process of solution)

Solve by substitution, simplify the third equation first

• x + z = 6 ⇒ x = 6 - z

Substitute the value of x into the first two equations

3(6 - z) + 4y + z = 32

    ⇒ 18 - 3z + 4y + z = 32

    ⇒ 4y - 2z = 14

    ⇒ 2y - z = 7

    ⇒ z = 2y - 7

2(6 - z) + 5y + 7z = 37

     ⇒ 12 - 2z + 5y + 7z = 37

     ⇒ 5y + 5z = 25

     ⇒ y + z = 5

Solve by substitution again to get

• y + 2y - 7 = 5
• 3y = 12
• y = 4

Find z

• z = 2*4 - 7 = 1

Find x

• x = 6 - 1 = 5

The solution is

• (5, 4, 1)

Correct choice is B