Question

Problem: an old book listed that 72 turkeys were bought for $\$\square.\square\square$ each, at a total cost of $\$\square 67.9\square.$ what was the cost of each turkey, if each $\square$ stands for a digit that was unreadable in the old book

Answer 1

72 turkeys were bought at $5.11 each for a total cost of $367.92.

Explanation:

Trial and error isn't so difficult for this problem. The final price will be an even number of cents. Without those pennies added, the price per turkey must be below an integer number of cents, but within 1/8 cent of that integer number.

• 167.90/72 = 2.3319... (too high)
• 267.90/72 = 3.7208... (too high)
• 367.90/72 = 5.1097... good candidate
• 467.90/72 = 6.4986... (too low)
• 567.90/72 = 7.8875 (too low)
• 667.90/72 = 9.2763... (too low)

For higher first digits of the total cost, the per-turkey cost is more than 3 digits.

For our "good candidate", the per-turkey cost will be $5.11, so the total bill will be $5.11×72 = $367.92 . . . . matches the required digits.