Antonio$$s Car Services provides maintenance services for motorized vehicles. In March $2024,$ Rick placed an order for a new set of tires for $$440.$ When a customer purchases goods or services in excess of $$400,$ Antonio$$s gives the customer a $20\%$ discount coupon for future purchases made in the next three months. Antonio$$s estimates that approximately $75\%$ of customers utilize the coupon and that on average those customers will purchase goods or services that typically sell for $$80.$

Required:

$($a$)$ How many performance obligations are in Rick$$s contract?

$($b$)$ Prepare a journal entry to record revenue for this transaction, assuming that Antonio$$s uses the residual method to estimate the stand$-$alone selling price of new tires sold without the discount coupon.