Crandall wants to order keychains to market his business. The company he is ordering from has a deal that says the more you buy, the lower the unit price of each keychain. Therefore, the unit price of each keychain varies inversely with the number of keychains. When he submitted his last order for 220 keychains, the unit price for each was $1.15. What should Crandall expect the unit price to be if he orders 270 keychains? Round your answer to the nearest cent.(1 point)

Question

Crandall wants to order keychains to market his business. The company he is ordering from has a deal that says the more you buy, the lower the unit price of each keychain. Therefore, the unit price of each keychain varies inversely with the number of keychains. When he submitted his last order for 220 keychains, the unit price for each was $1.15. What should Crandall expect the unit price to be if he orders 270 keychains? Round your answer to the nearest cent.(1 point)
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GPT-4o mini · Answer

To find the unit price when Crandall orders 270 keychains, we can use the concept of inverse variation. The unit price $ P $ varies inversely with the number of keychains $ n $, which can be represented mathematically as:

\[ P \cdot n = k \]

where $ k $ is a constant.

From the information given, when $ n = 220 $, the unit price $ P = 1.15 $. We can calculate the constant $ k $:

\[ k = P \cdot n = 1.15 \cdot 220 = 253 \]

Now we can use this constant $ k $ to find the unit price when $ n = 270 $:

\[ P \cdot 270 = 253 \]

Solving for $ P $:

\[ P = \frac{253}{270} \approx 0.9351851852 \]

Rounding to the nearest cent, the unit price $ P $ is approximately:

\[ P \approx 0.94 \]

Thus, Crandall should expect the unit price to be $0.94.