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28 Nov 2024, 19:16
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It's more efficient to calculate the price per dozen, given that's what the question is focused around (e.g. price of dozen eggs differs by $1).
In fact, if we arrive at the previous statement \frac{144}{x} = \frac{144}{x-2} + 1
We can then quickly search for factors of 144 that differ by 1. The prime factorization of 144 is 3^2 * 2^4. Eyeballing, 8 and 9 are factors that differ by one, and 16 and 18 are the corresponding answer choices. If we want to find the solution that includes the free eggs, we look for the smaller number (because 2 eggs were free). Answer is 16.
In fact, if we arrive at the previous statement \frac{144}{x} = \frac{144}{x-2} + 1
We can then quickly search for factors of 144 that differ by 1. The prime factorization of 144 is 3^2 * 2^4. Eyeballing, 8 and 9 are factors that differ by one, and 16 and 18 are the corresponding answer choices. If we want to find the solution that includes the free eggs, we look for the smaller number (because 2 eggs were free). Answer is 16.
einstein801
