Question
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A certain shampoo is available in two sizes. A 23.7 -ounce bottle costs \( \$ 4.97 \). A 33.8 -ounce bottle costs \( \$ 7.48 \). Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent. \( \begin{array}{l}\text { Unit price for the } 23.7 \text {-ounce bottle: } \$ \square \text { per ounce } \\ \text { Unit price for the } 33.8 \text {-ounce bottle: } \$ \square \text { per ounce } \\ \text { The better buy: } \\ \text { The } 23.7 \text {-ounce bottle } \\ \text { O The } 33.8 \text {-ounce bottle }\end{array} \)

Ask by Edwards Summers. in the United States
Jan 13,2025

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Tutor-Verified Answer

Answer

The 23.7-ounce bottle costs \$0.21 per ounce, and the 33.8-ounce bottle costs \$0.22 per ounce. Therefore, the 23.7-ounce bottle is the better buy.

Solution

To determine which shampoo bottle offers the better value, we'll calculate the unit price (price per ounce) for each size and compare them. ### Calculations: 1. **23.7-ounce bottle:** \[ \text{Unit Price} = \frac{\$4.97}{23.7 \text{ oz}} \approx \$0.21 \text{ per ounce} \] 2. **33.8-ounce bottle:** \[ \text{Unit Price} = \frac{\$7.48}{33.8 \text{ oz}} \approx \$0.22 \text{ per ounce} \] ### Summary: \[ \begin{array}{l} \text{Unit price for the } 23.7 \text{-ounce bottle: } \$0.21 \text{ per ounce} \\ \text{Unit price for the } 33.8 \text{-ounce bottle: } \$0.22 \text{ per ounce} \\ \text{The better buy: } \\ \text{The } 23.7 \text{-ounce bottle} \\ \text{O The } 33.8 \text{-ounce bottle} \end{array} \] ### Conclusion: **The 23.7-ounce bottle is the better buy** because it has a lower unit price of \$0.21 per ounce compared to the 33.8-ounce bottle's \$0.22 per ounce.

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The Deep Dive

To find the unit prices, we divide the cost of each bottle by its size in ounces. For the 23.7-ounce bottle: \[ \text{Unit price} = \frac{4.97}{23.7} \approx 0.21 \] So, the unit price for the 23.7-ounce bottle is approximately **$0.21 per ounce**. For the 33.8-ounce bottle: \[ \text{Unit price} = \frac{7.48}{33.8} \approx 0.22 \] Thus, the unit price for the 33.8-ounce bottle is approximately **$0.22 per ounce**. Comparing the two: The better buy is the **23.7-ounce bottle**.

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