In April $2$XX$0,$ Useful Tech Company acquired $100$ percent of the common stock of Royalty Company by paying $150,000$ cash and promising to pa an additional amount if certain earnings targets were met. The fair value of the contingent consideration was $15,830.$ Immediately after the acquistion, Useful changed its name to Royalty Tech Incorporated. According to its June $30,2$XX$0$ SEC Form $10-$Q$,$ on the acquistion date, the total fair value assigned to tangible and intangible assets axquired $($excluding goodwill$)$ was $194,225$ million, while the total fair value assigned to liabilities assumed was $132,740$ million.

a$.$ What is the total acquistio cost $($i$.$e$.,$ purchease price$)$ of the acquistion?

b$.$ What is the value of goodwill recognized in Royalty Tech inc.$\text{'}$s consolidated financial statements as a result of this acquistion?