Question

When compact discs are sold at $13 each, hmv can sell 300 in a month. for every $2 increase in the number of cd’s sold drops by 30.

Answer 1

The number of compact discs (CDs) sold by hmv, priced at $13 each, is given by the equation
`\(N = 300 - 30 \cdot ((x-300))/(2)\), where \(x\)`is the increase in the number of CDs sold.

Step-by-step explanation:

The given problem states that when CDs are sold at $13 each, hmv can sell 300 in a month. For every $2 increase in the number of CDs sold, the total number of CDs sold drops by 30. Let's denote the increase in the number of CDs sold by \(x\). The total number of CDs sold (\(N\)) is given by
`\(N = 300 - 30 \cdot (x)/(2)\).`

The equation can be explained as follows:

- The initial number of CDs sold, when
`\(x = 0\), is \(300 - 30 \cdot (0)/(2) = 300\).`

- For each $2 increase in \(x\), the total number of CDs sold drops by 30.

- The term
`\((x)/(2)\)` represents the number of $2 increases in CDs sold. Multiplying it by 30 accounts for the drop in CDs sold for each $2 increase.

- Subtracting this term from 300 gives the total number of CDs sold.

For example, if \(x = 2\), there is a $4 increase, and the total number of CDs sold is
`\(300 - 30 \cdot (2)/(2) = 270\)`. If
`\(x = 4\)`, there is a $8 increase, and the total number of CDs sold is
`\(300 - 30 \cdot (4)/(2) = 240\`, and so on.