Bernard bought a painting for $3600. Lucas bought a similar paintingthat cost 35% more than Bernard's painting. How much money did Lucaspay for his painting?

1. Break Down the Problem

1. Determine the cost of Lucas's painting relative to Bernard's painting.
2. Calculate the additional amount Lucas paid compared to Bernard's purchase.

2. Relevant Concepts

The total cost of Lucas's painting can be calculated using the formula:
$\text{Cost of Lucas's painting} = \text{Cost of Bernard's painting} + \text{Additional cost}$
Where the additional cost is based on Bernard's painting price increased by 35%. This can be calculated as:
$\text{Additional cost} = 0.35 \times \text{Cost of Bernard's painting}$

3. Analysis and Detail

1. First, calculate the additional cost.
   $\text{Additional cost} = 0.35 \times 3600 = 1260$
2. Now, calculate the total cost for Lucas's painting.
   $\text{Cost of Lucas's painting} = 3600 + 1260 = 4860$

4. Verify and Summarize

Verify the calculations to ensure they are accurate:

1. The additional amount calculated is correct: $1260.
2. The final cost for Lucas's painting is confirmed as $4860.

Final Answer

Lucas paid $4860 for his painting.