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

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Answer 1

The relationship between the number of keychains ordered and the unit price can be modeled using the equation for inverse variation:

\[ P \times Q = k \]

where:

• \( P \) is the unit price,
• \( Q \) is the quantity of keychains, and
• \( k \) is a constant.

From the information given, when Crandall ordered 220 keychains at $1.15 each, we can calculate the constant \( k \):

\[ k = P \times Q = 1.15 \times 220 \]

Calculating \( k \):

\[ k = 1.15 \times 220 = 253 \]

Now, we want to find the new unit price (\( P' \)) when Crandall orders 270 keychains (\( Q' = 270 \)).

Using the constant \( k \):

\[ P' \times Q' = k \]

Substituting the known values:

\[ P' \times 270 = 253 \]

To solve for \( P' \):

\[ P' = \frac{253}{270} \]

Calculating \( P' \):

\[ P' \approx 0.9351851852 \]

Rounding to the nearest cent:

\[ P' \approx 0.94 \]

Therefore, the expected unit price for each keychain if Crandall orders 270 keychains is $0.94.