There is a new apartment complex in town that offers two types of units at same price per type of unit: one-bedroom units and two-bedroom units. Alpha Ltd decides to rent two one-bedroom units and two two-bedroom units. They pay a total of BWP 5 600 for the month. Beta Ltd rents three one-bedroom units and one two-bedroom unit in the same complex. They pay a total of BWP 4 800 for the month. Calculate the monthly rent for a one-bedroom unit and a two-bedroom unit.             

We can solve this problem using a system of linear equations. Let:

- \( x \) represent the monthly rent for a one-bedroom unit.
- \( y \) represent the monthly rent for a two-bedroom unit.

### Step 1: Set up the equations
From the problem, we have two scenarios:

1. **Alpha Ltd** rents 2 one-bedroom units and 2 two-bedroom units for BWP 5,600.
   This gives the equation:
   \[
   2x + 2y = 5600
   \]
   
2. **Beta Ltd** rents 3 one-bedroom units and 1 two-bedroom unit for BWP 4,800.
   This gives the equation:
   \[
   3x + y = 4800
   \]

### Step 2: Simplify the equations
- From the first equation, divide both sides by 2 to simplify:
  \[
  x + y = 2800
  \]
  So, we now have:
  \[
  x + y = 2800 \tag{1}
  \]
  
- The second equation remains as:
  \[
  3x + y = 4800 \tag{2}
  \]

### Step 3: Solve the system of equations
We can use substitution or elimination. Let's use substitution. From equation (1), solve for \( y \):
\[
y = 2800 - x \tag{3}
\]

Substitute equation (3) into equation (2):
\[
3x + (2800 - x) = 4800
\]

### Step 4: Solve for \( x \)
Simplify the equation:
\[
3x + 2800 - x = 4800
\]
\[
2x + 2800 = 4800
\]
\[
2x = 4800 - 2800
\]
\[
2x = 2000
\]
\[
x = 1000
\]

### Step 5: Solve for \( y \)
Substitute \( x = 1000 \) into equation (1):
\[
1000 + y = 2800
\]
\[
y = 2800 - 1000
\]
\[
y = 1800
\]

### Conclusion:
- The monthly rent for a one-bedroom unit is **BWP 1,000**.
- The monthly rent for a two-bedroom unit is **BWP 1,800**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What would be the total rent for renting 4 one-bedroom units?
2. If Gamma Ltd rents 5 two-bedroom units, what would be their total rent?
3. What would be the rent for a combination of 3 one-bedroom units and 4 two-bedroom units?
4. How would the total cost change if the rent for two-bedroom units increased by 10%?
5. How many two-bedroom units could be rented with a budget of BWP 7,200?

**Tip:** When solving systems of equations, always check if substitution or elimination is easier based on the coefficients.

There is a new apartment complex in town that offers two types of units at same price per type of unit: one-bedroom units and two-bedroom units. Alpha Ltd decides to rent two one-bedroom units and two two-bedroom units. They pay a total of BWP 5 600 for the month. Beta Ltd rents three one-bedroom units and one two-bedroom unit in the same complex. They pay a total of BWP 4 800 for the month. Calculate the monthly rent for a one-bedroom unit and a two-bedroom unit.

Learn how to calculate the monthly rent for one-bedroom and two-bedroom units using systems of linear equations. Alpha Ltd rents 2 one-bedroom and 2 two-bedroom units for BWP 5,600, while Beta Ltd rents 3 one-bedroom and 1 two-bedroom unit for BWP 4,800. Step-by-step solution provided, suitable for Grades 9-11.

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