A customer wants to purchase three cans of paint. Each can is priced at $29.00. The customer has a coupon for $15 off his purchase. The sales tax is 8% and is applied after the discount has been applied. What is the total purchase amount?

The total cost before the discount is 3 cans * $29.00 per can = $<<3*29=87>>87.00.

After the $15.00 coupon, the total cost is now $87.00 - $15.00 = $<<87-15=72>>72.00.
Sales tax is 8% * $72.00 = $<<8*.01*72=5.76>>5.76.
After tax, the total purchase amount is $72.00 + $5.76 = $<<72+5.76=77.76>>77.76. Answer: \boxed{77.76}.

To calculate the total purchase amount, you will need to follow these steps:

Step 1: Determine the cost of each can of paint
Each can is priced at $29.00.

Step 2: Calculate the subtotal before the discount
Since the customer wants to purchase three cans of paint, you need to multiply the cost of each can by the number of cans:
Subtotal = Cost of each can x Number of cans
Subtotal = $29.00 x 3 = $87.00

Step 3: Apply the discount
The coupon value is $15.00, so subtract it from the subtotal:
Subtotal - Discount = Total before tax
$87.00 - $15.00 = $72.00

Step 4: Calculate the amount of sales tax
The sales tax is 8% of the total before tax:
Sales Tax = Total before tax x Tax rate
Sales Tax = $72.00 x 0.08 = $5.76

Step 5: Add the sales tax to the total before tax
Total purchase amount = Total before tax + Sales tax
Total purchase amount = $72.00 + $5.76 = $77.76

Therefore, the total purchase amount is $77.76.

To calculate the total purchase amount, we can follow these steps:

Step 1: Determine the original price of the three cans of paint.
Each can is priced at $29.00, so the original price of all three cans would be: 3 cans * $29.00 = $87.00.

Step 2: Subtract the discount amount from the original price.
The customer has a coupon for $15 off the purchase, so we subtract $15.00 from $87.00 to find the discounted price: $87.00 - $15.00 = $72.00.

Step 3: Calculate the sales tax on the discounted price.
The sales tax is 8%, so we need to find 8% of $72.00.
To do this, we multiply $72.00 by 8% (or 0.08): $72.00 * 0.08 = $5.76.

Step 4: Add the discounted price and the sales tax to find the total purchase amount.
To find the total purchase amount, we add the discounted price ($72.00) and the sales tax ($5.76): $72.00 + $5.76 = $77.76.

Therefore, the total purchase amount is $77.76.