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Which equation would help determine the cost of 10 boolis? Chuse 1 answere (1) \( \frac{x}{10}=\frac{8}{\$ 19.60} \) (B) \( \frac{10}{\$ 19.60}=\frac{x}{8} \) (C) \( \frac{8}{10}=\frac{x}{\$ 19.60} \) (D) \( \frac{10}{8}=\frac{\$ 19.60}{x} \) (I) None of the above

Ask by Davison Blake. in the United States
Jan 24,2025

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Tutor-Verified Answer

Answer

None of the provided equations correctly determine the cost of 10 boolis.

Solution

To determine the cost of 10 boolis given that 8 boolis cost \$19.60, we can set up a proportion based on the cost per booli. 1. **Find the cost per booli:** \[ \text{Cost per booli} = \frac{\$19.60}{8} = \$2.45 \text{ per booli} \] 2. **Calculate the cost for 10 boolis:** \[ \text{Cost for 10 boolis} = 10 \times \$2.45 = \$24.50 \] Now, let's examine the provided options to see which one correctly represents this proportion: - **(A) \( \frac{x}{10} = \frac{8}{\$19.60} \)** - Solving this gives \( x = \frac{10 \times 8}{19.60} \approx \$4.08 \), which is incorrect. - **(B) \( \frac{10}{\$19.60} = \frac{x}{8} \)** - Solving this also gives \( x \approx \$4.08 \), which is incorrect. - **(C) \( \frac{8}{10} = \frac{x}{\$19.60} \)** - Solving this gives \( x = \frac{8 \times 19.60}{10} = \$15.68 \), which is incorrect. - **(D) \( \frac{10}{8} = \frac{\$19.60}{x} \)** - Solving this gives \( x = \frac{19.60 \times 8}{10} = \$15.68 \), which is also incorrect. None of the provided equations correctly represent the proportion needed to determine the cost of 10 boolis as \$24.50. **Answer:** **(I) None of the above**

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The Deep Dive

If we want to determine the cost of 10 boolis based on the cost of 8, we can set it up using proportions. The correct method to find the equivalent cost involves using option (B): \( \frac{10}{\$ 19.60} = \frac{x}{8} \). This allows us to find the cost for 10 boolis by scaling it up from the cost of 8. In real-world terms, this type of proportion is frequently used in budgeting scenarios. For instance, if a box of 8 snacks costs $19.60, you might want to quickly calculate how much it would cost to buy 10 or even 20 snacks. Setting up a simple proportion allows you to make those calculations quickly without a calculator!

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