# Step-by-Step Solution Let's break the problem and what is given what is being. ## Given - **Income** (\( I \)): \$500 - **Price of a book** (\( P_B \)): \$10 - **Value of \( B \)**: 50 (This likely means the consumer can buy 50 books with their income.) - **Unknown**: **Price of a DVD** (\( P_D \)) ## Step 1: Interpret the Value of \( B = 50 \) If \( B \) is the maximum number of books that can be bought with the income, then: \[ B = \frac{I}{P_B} \] Plug in the values: \[ B = \frac{500}{10} = 50 \] This matches the given value of \( B \), confirming our interpretation. ## Step 2: Find the Price of a DVD Since only the information about books is given directly, we need more information about DVDs. Usually, if one good (books) can be bought up to 50 units, and the other good (DVDs) can be bought up to \( D \) units, then: \[ D = \frac{I}{P_D} \] But we are not given a value for \( D \). However, if the problem is asking **what is the price of a DVD**, and we only know about books, **there is not enough information to uniquely determine \( P_D \)** unless we are missing something. ## Step 3: Review for Possible Missing Information - If there is a typo or missing info, such as a value for \( D \) (maximum DVDs purchasable), then we could solve for \( P_D \) using the same method as with books. - For example, **if the value of \( D \) is also given as 50** (i.e., the consumer can also buy 50 DVDs with their income), then: \[ D = \frac{500}{P_D} = 50 \implies P_D = \frac{500}{50} = 10 \] So, the price of a DVD would also be \$10. ## Final Answer **With only the information provided, we cannot solve for the price of a DVD unless the maximum number of DVDs purchasable is also specified.** --- ### Summary Table | Variable | Value | Equation Used | |------------------|----------|------------------------------| | Income (\(I\)) | \$500 | — | | Price of Book (\(P_B\)) | \$10 | — | | Max Books (\(B\))| 50 | \(B = \frac{I}{P_B}\) | | Price of DVD (\(P_D\)) | **Unknown** | \(D = \frac{I}{P_D}\) | --- ## **Conclusion** > **The price of a DVD cannot be determined from the information given. If the number of DVDs that can be bought (\( D \)) is provided, then the price can be calculated as:** > > \[ > P_D = \frac{500}{D} > \] > **Otherwise, more information is needed.**