Official Solution:A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?
A. 8
B. 12
C. 15
D. 16
E. 18
Say the # of eggs the cook originally got was \(x\);
The price per egg then would be \(\frac{12}{x}\) and the price per dozen would be \(12*\frac{12}{x}\).
Now, since the cook talked the seller into adding two more eggs then he finally got \(x+2\) eggs (notice that \(x+2\) is exactly what we should find);
So, the price per egg became \(\frac{12}{x+2}\) and the price per dozen became \(12*\frac{12}{x+2}\).
As after this the price per dozen went down by a dollar then \(12*\frac{12}{x}-12*\frac{12}{x+2}=1\), which simplifies to \(\frac{144}{x}-\frac{144}{x+2}=1\). At this point it's better to substitute the values from answer choices rather than to solve for \(x\). Answer choices E fits: if \(x+2=18\) then \(\frac{144}{16}-\frac{144}{18}=9-8=1\).
Answer: E
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