The shilling was $\frac1{20}$ of a pound; $\frac1{20}=0.05$, and a pound is $100$ new pence, so one shilling is $5$ new pence. Thus, $17$ shillings is $17\cdot 5=85$ new pence or £$0.85$. In general, $n$ shillings are $5n$ new pence or $0.05n$ pounds.
The old penny is $\frac1{12}$ of a shilling, so it’s $\frac1{12}$ of $5$ new pence, i.e., $\frac5{12}$ of a new penny. $9$ old pence is therefore $9\cdot\frac5{12}=\frac{15}4=3.75$ new pence, or $0.0375$ pounds.
Put the pieces together, any you have $7.00+0.85+0.0375=7.8875$ pounds, which rounds to £$7.89$. The same approach will allow you to convert any old-style amount to the modern decimal form.