Five apples and four oranges cost $\$ 11.80$. One apple and six oranges cost $\$ 9.90$. How much does one orange cost? \[ \$ \]

Step 1 ：Let's represent the problem with the following equations, where 'a' represents the cost of one apple and 'o' represents the cost of one orange:

Step 2 ：\[5a + 4o = 11.80\]

Step 3 ：\[a + 6o = 9.90\]

Step 4 ：We can solve this system of equations to find the cost of one orange.

Step 5 ：The solution to the system of equations is \(a = 1.20\) and \(o = 1.45\).

Step 6 ：So, the cost of one orange is \(\boxed{1.45}\).