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?
old cds = x
new cds = 2.5x
4old cds + 9 new cds = 159
4(x) + 9(2.5x)=159
4x+22.5x=159
26.5x=159
x=6 so old cds cost $6.
and new cds cost 2.5(6)=$15.
Check:
4(6)+9(15)=159
24+ 135 =159
159=159
To find the price of each item, let's assign variables to the prices. Let X represent the price of a used CD, and 2.5X represent the price of a new CD.
Given that 4 used CDs and 9 new CDs cost $159, we can set up an equation based on this information.
The total cost of the used CDs is 4X, and the total cost of the new CDs is 9(2.5X) or 22.5X. According to the problem, the total cost of all the CDs is $159.
So, the equation we have is: 4X + 22.5X = 159.
Combining like terms, we get: 26.5X = 159.
To solve for X, divide both sides of the equation by 26.5: X = 159 / 26.5.
X ≈ 6.00.
So, the price of a used CD is approximately $6.00.
To find the price of a new CD, multiply the price of a used CD (X) by 2.5: 6.00 x 2.5 = 15.00.
Therefore, the price of a new CD is $15.00.
In summary, the price of each item is approximately $6.00 for a used CD and $15.00 for a new CD.