Please reason step by step, and put your final answer within \boxed{}.
Louis is making himself a velvet suit for a high-end gala. The velvet fabric he chose costs $24 per yard. He purchases a pattern for $15, two spools of silver thread for $3 each, lining fabric at an unknown price per yard, a set of 12 stylish buttons for $14, and 3 yards of exquisite trim for $19 per yard. Additionally, he has a 10% discount coupon specific to fabrics, which he applies only to the velvet and lining fabric. He spent a total of $310.50 after applying the discount. If Louis bought 5 yards of velvet fabric and 4 yards of lining fabric, what is the cost per yard of the lining fabric?
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