Brittany's family went to dinner at her favorite restaurant because her father had a coupon for 15% off. Her father said if she could correctly figure out the total cost of dinner, including the 5% sales tax, he would take them all out for frozen yogurt on the way home. The meal cost $64.00 without the discount. Brittany determined the total, with the discount and sales tax, will be $58.12. Did Brittany figure it out correctly? Show your work to support your answer.