A record stores sells CDs for $12 each.A music club offers 5 free CDs and charges $15 for each additional CD.How many CDs would have to buy for cost to be the same?
To find out how many CDs you would have to buy for the cost to be the same, we need to calculate the total cost for both the record store and the music club.
Let's start with the record store:
The cost per CD is $12.
If you buy 'x' CDs, the total cost from the record store would be 12x dollars.
Now, let's move on to the music club:
The music club offers 5 free CDs, so for the first 5 CDs, the cost is $0.
For any additional CDs beyond the 5 free ones, the cost is $15 each.
If you buy 'y' additional CDs, the cost from the music club would be 15y dollars.
To find the total cost from the music club, we need to add the cost of the additional CDs to the cost of the 5 free CDs.
The cost for the first 5 CDs is $0, so the total cost from the music club would be 15y dollars.
To make the costs equal, we set the total cost from the record store equal to the total cost from the music club:
12x = 15y
Now, let's simplify this equation:
Divide both sides by 3:
4x = 5y
To find the values of 'x' and 'y' that satisfy this equation, we can start by assuming a value for 'x' and then calculate the corresponding value for 'y'.
For example, if we assume 'x' = 5 (which means buying 5 CDs from the record store), then the equation becomes:
4(5) = 5y
20 = 5y
y = 4
So, if you buy 5 CDs from the record store and 4 additional CDs from the music club, the total cost will be the same.
Let x = # of CDs.
12x = 15x - 60
60 = 3x
20 = x