To solve for the original cost of a pack of cookies, let's analyze the information given:
John buys 8 packs of cookies, and they are on sale for 50 cents off per pack. He spends a total of $20.
Let \( c \) represent the original cost of a pack of cookies. Since there is a discount of 50 cents, the cost he actually pays for each pack is \( c - 0.50 \).
Thus, when he buys 8 packs of cookies, he spends: \[ 8(c - 0.50) = 20 \]
Now, looking at the options provided:
- 8(c + 0.50) = 20 - This would imply he is paying more than the original price, which is incorrect.
- 8c - 0.50 = 20 - This does not account for the total spent after applying the discount; it doesn’t reflect the correct situation.
- 8(c - 0.50) = 20 - This is correct as it correctly represents the total cost after applying the discount.
- 8 - 0.50c = 20 - This equation does not represent the problem correctly.
Thus, the correct answer is: 8(c - 0.50) = 20.