A vendor at a concert sells new and used CDs. The new CDs cost 2.5 times as much as the old CDs. If 4 used CDs and 9 new CDs cost $159, what is the price of each item?
9N+4U=159
9(2.5U)+ 4U=159
solve for U first, then solve for N
To find the price of each type of CD, let's set up equations based on the given information:
Let's denote the price of a used CD as 'x'.
Then, the price of a new CD would be 2.5 times the price of a used CD, which is 2.5x.
Now, using the information that 4 used CDs and 9 new CDs cost $159, we can set up the equation:
4x + 9(2.5x) = 159
Simplifying the equation:
4x + 22.5x = 159
Combining like terms:
26.5x = 159
Dividing both sides of the equation by 26.5:
x = 159 / 26.5
Evaluating this:
x ≈ 6
So, the price of a used CD is approximately $6.
To find the price of a new CD, which is 2.5 times the price of a used CD:
2.5x = 2.5 * 6 = 15
Therefore, the price of a new CD is $15.