The electricity bill consists of a fixed component and a variable component. The average electricity bill in Ramesh's house amounts to Rs 1200 if he uses 150 units of current. It amounts to Rs 2480 if he uses 400 units of current. Find the amount(in rupees) that Ramesh has to pay if he uses 750 units of current.

Let the fixed component of the electricity bill be \( F \) (in rupees), and the variable component per unit of electricity be \( V \) (in rupees per unit).

The total electricity bill, \( B(x) \), when \( x \) units of electricity are used is given by the equation:

\[
B(x) = F + V \cdot x
\]

### Step 1: Set up the system of equations
From the given information:
1. When Ramesh uses 150 units of electricity, the bill is Rs 1200:
   \[
   F + V \cdot 150 = 1200 \quad \text{(Equation 1)}
   \]
2. When Ramesh uses 400 units of electricity, the bill is Rs 2480:
   \[
   F + V \cdot 400 = 2480 \quad \text{(Equation 2)}
   \]

### Step 2: Solve the system of equations
We can subtract Equation 1 from Equation 2 to eliminate \( F \):

\[
(F + V \cdot 400) - (F + V \cdot 150) = 2480 - 1200
\]

Simplifying:

\[
V \cdot 400 - V \cdot 150 = 1280
\]

\[
V \cdot (400 - 150) = 1280
\]

\[
V \cdot 250 = 1280
\]

\[
V = \frac{1280}{250} = 5.12
\]

So, the variable component is \( V = 5.12 \) rupees per unit.

### Step 3: Find the fixed component \( F \)
Now, substitute \( V = 5.12 \) into Equation 1 to find \( F \):

\[
F + 5.12 \cdot 150 = 1200
\]

\[
F + 768 = 1200
\]

\[
F = 1200 - 768 = 432
\]

So, the fixed component is \( F = 432 \) rupees.

### Step 4: Calculate the bill for 750 units
Now that we know both \( F = 432 \) and \( V = 5.12 \), we can calculate the bill for 750 units:

\[
B(750) = F + V \cdot 750 = 432 + 5.12 \cdot 750
\]

\[
B(750) = 432 + 3840 = 4272
\]

So, the amount Ramesh has to pay for using 750 units of electricity is Rs **4272**.

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Would you like more details on how I solved this, or do you have any questions?

Here are 5 related questions to explore:
1. How would the bill change if the fixed component increased by Rs 100?
2. What would happen if the price per unit of electricity (variable component) increased by 10%?
3. How can we represent this problem with a linear equation?
4. How can we use this model to predict the electricity bill for any number of units?
5. What are the assumptions behind the linear model for electricity billing?

**Tip:** When solving systems of equations, subtracting the equations (as done above) is a great way to eliminate one variable and simplify the process!

Learn how to calculate the electricity bill with both fixed and variable components based on unit usage. This problem shows how to set up and solve a system of linear equations to determine the amount Ramesh pays for 750 units of electricity, given the fixed and variable components. Suitable for students in Grades 9-11.

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