Let's break down the given problem step-by-step to find the cost per day for renting the car and LCD screen.

Given Information:

1. Total cost for 3 days: $12,256
2. Hall rental per day: $2,000
3. Car rental for 3 days: Between $1,500 and $2,700 (inclusive)
4. Cost per day for car and LCD screen rental must be whole numbers.

Steps to Find the Cost per Day:

1. Calculate the Total Hall Rental Cost for 3 Days: [ \text{Total hall rental cost} = 3 \times 2000 = 6000 , \text{USD} ]

2. Subtract the Hall Rental Cost from the Total Cost: [ \text{Remaining cost} = 12256 - 6000 = 6256 , \text{USD} ] This remaining amount is the combined total cost for renting the car and the LCD screen for 3 days.

3. Determine the Possible Cost Range for Car Rental: The car rental for 3 days is between $1,500 and $2,700. We can denote the car rental cost for 3 days as ( C ), where: [ 1500 \leq C \leq 2700 ]

4. Calculate the Cost for LCD Screen Rental: Let the total cost for the LCD screen rental for 3 days be ( L ). Then: [ C + L = 6256 ] Rearranging, we find: [ L = 6256 - C ]

   The daily costs for car rental and LCD screen rental, ( \frac{C}{3} ) and ( \frac{L}{3} ), must also be whole numbers. Thus, ( C ) must be divisible by 3.

Find the Correct Cost for Car Rental (C):

We will check values for ( C ) within the range [1500, 2700] that are divisible by 3:

[ \begin{align*} C = 1500, & \quad \text{since } 1500 \div 3 = 500 \ C = 1503, & \quad \text{since } 1503 \div 3 = 501 \ C = 1506, & \quad \text{since } 1506 \div 3 = 502 \ & \vdots \ C = 2700, & \quad \text{since } 2700 \div 3 = 900 \ \end{align*} ]

Determine the Corresponding LCD Screen Rental Costs:

We find a value for ( C ) such that ( L = 6256 - C ) is also divisible by 3. Let's check:

• If ( C = 2400 ): [ L = 6256 - 2400 = 3856, \quad \text{and} \quad 3856 \div 3 = 1285.33 , (\text{not a whole number}) ]

• If ( C = 1800 ): [ L = 6256 - 1800 = 4456, \quad \text{and} \quad 4456 \div 3 = 1485.33 , (\text{not a whole number}) ]

• If ( C = 1500 ): [ L = 6256 - 1500 = 4756, \quad \text{and} \quad 4756 \div 3 = 1585.33 , (\text{not a whole number}) ]

• If ( C = 2100 ): [ L = 6256 - 2100 = 4156, \quad \text{and} \quad 4156 \div 3 = 1385.33 , (\text{not a whole number}) ]

Continue until the cost combination is found which satisfies the integer requirements.