Due to economic surges the price of eggs suddenly reduced by 40%. This enabled…

Concept

When the money spent is fixed, the number of items bought varies inversely with the price per item: items = money / price. A price reduction of 40% means the new price is the remaining 60% of the original (reduced BY 40%, not reduced TO 40%).

Application

1. Let the original price per egg = x dollars. New price per egg = 60% of x = 0.6x.

2. Eggs for $50 at original price = 50/x. Eggs for $50 at reduced price = 50/(0.6x) = 250/(3x).

3. Extra eggs bought = 64, so 250/(3x) - 50/x = 64.

4. Combine over 3x: (250 - 150)/(3x) = 64, so 100/(3x) = 64, giving x = 100/192 = 25/48.

5. Reduced price per egg = 0.6x = 0.6 * 25/48 = 15/48 = 5/16 dollars.

6. Reduced price per dozen = 12 * 5/16 = 60/16 = 15/4 = $3.75.

Cross-check

At the reduced rate 5/16 per egg, $50 buys 50 / (5/16) = 160 eggs; at the original rate 25/48 per egg, $50 buys 50 / (25/48) = 96 eggs. The increase 160 - 96 = 64 matches the given condition, confirming $3.75 per dozen.