Let the cost of one orange be $x$. Since the cost of one mango is three times that of an orange, the cost of one mango will be $3x$.

Abby bought three mangoes and two oranges, so the total cost is:

$3(3x) + 2x = 385.65$

This simplifies to:

$9x + 2x = 385.65$

$11x = 385.65$

Now, solve for $x$:

$x = \frac{385.65}{11} = 35.06$

So, the cost of one orange is $35.06$. Since the cost of a mango is three times that of an orange, the cost of one mango is:

$3 \times 35.06 = 105.18$

Thus, the cost of one mango is $105.18.

Would you like more details or have any questions?

Here are 5 related questions you could explore:

1. How much did Abby spend on the oranges alone?
2. How much did Abby spend on the mangoes alone?
3. What would be the total cost if she bought five mangoes and four oranges?
4. If the price of an orange increased by 10%, what would be the new cost of a mango?
5. If Abby had only $500, how many mangoes could she buy?

Tip: When setting up a problem involving proportions, always express all unknowns in terms of a single variable to simplify the solution process.