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

We know that the unit price $ p $ varies inversely with the number of keychains $ n $. This relationship can be expressed as: $$ p \times n = k $$ where $ k $ is a constant. From the information given, when Crandall orders 220 keychains, the unit price is $1.15. We can first find the constant $ k $: $$ k = p \times n = 1.15 \times 220 $$ Calculating this: $$ k = 1.15 \times 220 = 253 $$ Now we need to find the expected unit price $ p $ when Crandall orders 270 keychains: $$ p \times 270 = k $$ Substituting the value of $ k $: $$ p \times 270 = 253 $$ Now, solve for $ p $: $$ p = \frac{253}{270} $$ Calculating this gives: $$ p \approx 0.9351851852 $$ Rounding to the nearest cent: $$ p \approx 0.94 $$ Thus, the expected unit price if Crandall orders 270 keychains is: $$ \boxed{0.94} $$