6. Andrea exchanged three books for seven CDs. (a) What are the two rates (ratios) implied by this statement? (b) How many CDs could she have exchanged at the same rate for 9 books?

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UpStudy AI · Accepted Answer

**Step 1. Identify the Given Exchange**

Andrea exchanged $$ 3 $$ books for $$ 7 $$ CDs.

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**Step 2. Determine the Two Implied Rates**

- **Rate in CDs per book:**  
  This is given by the ratio of CDs to books:  
  $$
  \frac{7 \text{ CDs}}{3 \text{ books}} = \frac{7}{3}
  $$

- **Rate in Books per CD:**  
  This is given by the ratio of books to CDs:  
  $$
  \frac{3 \text{ books}}{7 \text{ CDs}} = \frac{3}{7}
  $$

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**Step 3. Calculate the Number of CDs for 9 Books**

Using the rate of CDs per book $$\left(\frac{7}{3}\right)$$:

$$
\text{CDs} = 9 \text{ books} \times \frac{7 \text{ CDs}}{3 \text{ books}} = \frac{9 \times 7}{3} = \frac{63}{3} = 21 \text{ CDs}
$$

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**Final Answers:**

- **(a)** The two rates are $$\frac{3}{7}$$ (books per CD) and $$\frac{7}{3}$$ (CDs per book).
- **(b)** At the same rate, Andrea could have exchanged $$9$$ books for $$21$$ CDs.
**(a)** The two rates are 3 books per 7 CDs and 7 CDs per 3 books. **(b)** Andrea could exchange 9 books for 21 CDs.

Andrea exchanged three books for seven CDs.
(a) What are the two rates (ratios) implied by this statement?
(b) How many CDs could she have exchanged at the same rate for 9 books?

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