Let the amount Joshua originally paid for the bike be $P$.

Joshua sold the bike for 10% less than what he paid, which means he sold it for 90% of $P$. So, the equation representing this situation is:

$0.9P = 585$

To find $P$, divide both sides of the equation by 0.9:

$P = \frac{585}{0.9}$

Now, calculate $P$:

$P = 650$

So, Joshua originally paid $650 for the bike.

Would you like more details or have any other questions? Here are five related questions for further exploration:

1. How do you calculate percentages of a number?
2. If Joshua had sold the bike for 20% less, how much would he have received?
3. How can you use the concept of percentages to find the original price when given the sale price?
4. What is the formula for calculating a percentage decrease?
5. How would the problem change if he sold the bike for $650 instead?

Tip: When working with percentages, remember that multiplying by a percentage (as a decimal) can help quickly find the reduced or increased value.