How can I work out the charge per unit of electricity in this Question
The Question state.The charge for electricity consumption, E is partly constant and partly varies as the number,N of units used.The charge for 163 units is #453.80 while the charge for 42 units is #139.20.
Calculate the charge per unit of electricity.
To calculate the charge per unit of electricity, you need to determine the constant charge and the variable charge.
Let's assume the constant charge is "C" and the charge per unit of electricity is "x".
From the given information, we can set up two equations:
1) C + 163x = 453.80
2) C + 42x = 139.20
Now, we can solve these equations to find the values of C and x.
Subtracting equation 2 from equation 1, we get:
(163x - 42x) = (453.80 - 139.20)
121x = 314.60
Divide both sides of the equation by 121:
x = 314.60 / 121
x ≈ 2.60
Now, substitute the value of x into either of the original equations to solve for C:
C + 163(2.60) = 453.80
C + 424.80 = 453.80
C = 453.80 - 424.80
C = 29.00
Therefore, the constant charge (C) is 29.00 and the charge per unit of electricity (x) is approximately 2.60.
Hence, the charge per unit of electricity is #2.60.
To calculate the charge per unit of electricity, you can use the given information about the charges for different numbers of units used.
First, you can calculate the constant part of the charge by subtracting the variable part from the total charge for the given number of units.
For example:
- For 163 units: Total charge = #453.80, Variable charge = 163 * Charge per unit
- So, Constant charge = Total charge - Variable charge = #453.80 - (163 * Charge per unit)
Next, you can use the charges for the other given number of units to form another equation.
- For 42 units: Total charge = #139.20, Variable charge = 42 * Charge per unit
- So, Constant charge = Total charge - Variable charge = #139.20 - (42 * Charge per unit)
You now have two equations for the constant charge. You can set them equal to each other and solve for the Charge per unit of electricity.
(#453.80 - 163 * Charge per unit) = (#139.20 - 42 * Charge per unit)
Now, you can solve this equation to find the Charge per unit of electricity.