Nayan Patel purchases a compact vehicle with an MSRP of $17,980.00, including the destination charge and title fee. He selects a 4-way power front passenger seat, which costs 8 times the amount of remote keyless entry. The total cost of the compact vehicle, including a 7.2% sales tax, is $20,000.00. Find the cost of the remote keyless entry.
+33665 First find the price before sales tax:
P = $20000/1.072
The difference between this and the MSRP must equal nine times the cost of the remote keyless entry (4-way power passenger seat + keyless entry), so:
9*K = P - 17980 where K is cost of keyless entry.
9*K = 20000/1.072 - 17980
$${\mathtt{K}} = {\frac{\left({\frac{{\mathtt{20\,000}}}{{\mathtt{1.072}}}}{\mathtt{\,-\,}}{\mathtt{17\,980}}\right)}{{\mathtt{9}}}} \Rightarrow {\mathtt{K}} = {\mathtt{75.190\: \!713\: \!101\: \!160\: \!862\: \!4}}$$
or K ≈ $75
.
+33665 First find the price before sales tax:
P = $20000/1.072
The difference between this and the MSRP must equal nine times the cost of the remote keyless entry (4-way power passenger seat + keyless entry), so:
9*K = P - 17980 where K is cost of keyless entry.
9*K = 20000/1.072 - 17980
$${\mathtt{K}} = {\frac{\left({\frac{{\mathtt{20\,000}}}{{\mathtt{1.072}}}}{\mathtt{\,-\,}}{\mathtt{17\,980}}\right)}{{\mathtt{9}}}} \Rightarrow {\mathtt{K}} = {\mathtt{75.190\: \!713\: \!101\: \!160\: \!862\: \!4}}$$
or K ≈ $75
.
