Final answer:
The correct equation to represent the total cost after applying a 20% discount on a $68 purchase is 0.8(68) = T. This reflects paying 80% of the original price after the discount.
Step-by-step explanation:
Mike is using a coupon for 20% off his total purchase, which is $68. To represent the total cost after the discount with a variable T, we want to subtract the discount from the original price:
The 20% discount of the original price is calculated as 0.2 multiplied by $68, which equal to $13.6. Therefore, the equation representing the total cost after the discount (T) is obtained by subtracting the discount from the original price.
Option A: 69 - 0.2(68) = T is incorrect due to the wrong original price (should be 68, not 69).
Option B: 68 - .20 = T is incorrect because it subtracts 20 cents, not 20 percent.
Option C: 68 - 20 = T is incorrect because it subtracts $20, not 20 percent.
Option D: 0.8(68) = T is the correct representation since taking 20% off is the same as paying 80% of the original price.
The last option: 0.2(68) = T gives us the amount of the discount, not the total cost after the discount.