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A discount music store has a one-day sale onall vinyl albums. In order to purchase fromthe store, each customer must have a yearlymembershipCost of Vinyl AlbumsNumber ofVinyl AlbumsTotal Cost withMembership$35.004I7$57.509$72.50How much does the music store charge for ayearly membership?

User Sebastian Dine
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21 votes
21 votes
Music yearly membership

We want to know what part of the total cost of vinyl albums is due to the cost of the membership.

We know there are two parts of the price costumers have to pay:

1. yearly membership: Y

2. vinyls: X

We can find the cost due to the vinyls multiplying the cost of each one by the number of vinyls.

For 4 vinyls, the cost due to it is 4X

For 7, it is 7X

For 9, it is 9X

This means that the total cost of vinyl albums is

cost due to vinyls + yearly membership = total cost

For 4 vinyls, the total cost is $35.00, then

4X + Y = $35.00

For 7, the total cost is $57.50, then

7X + Y = $57.50

For 9, the total cost is $72.50, then

9X + Y = $72.50

Using the first two equations:

4X + Y = $35.00

7X + Y = $57.50

we are going to find Y.

Clearing X from the first equation:


\begin{gathered} 4X+Y=35.00 \\ 4X=35.00-Y \\ X=(35.00-Y)/(4) \end{gathered}

We replace this value of X in the second equation:


\begin{gathered} 7X+Y=57.50 \\ (7)/(4)(35.00-Y)+Y=57.50 \\ 61.25-1.75Y+Y=57.50 \\ 61.25-0.75Y=57.50 \\ -0.75Y=57.50-61.25 \\ -0.75Y=-3.75 \\ Y=-(3.75)/(-0.75) \\ Y=5 \end{gathered}

Then, the yearly membership cost is $5

Answer. A: $5.00

User Ankit Agarwal
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