The amount collected per month from a consumer of electrical power consists of two parts- a fixed charge for providing the service and a variable charge which is directly proportional to the number of units of power consumed. An amount of Rs. 700 is collected from the consumer when he consumed 50 units in a month. It is also noticed that when the consumption increases from 100 units per month to 200 units per month, the bill amount increases to 5/4 times that of the former. How much is the fixed charge per month?
Explain how to do this. Please
Hello Steve
Can this be a possible way.
F + 100V = 4/5 (F + 200V)
By solving
F/V = 300
F/6 = 50V
F + 50V = 700
F + F/6 = 700
7F/6 = 700
F = 600
So, the fixed charge is 600
Ah, yes. You are correct. I had misread the problem.
Good work.
How did you get F/6=50V
If F=300v,
Then F/6=300v/6
F/6=50v
Well, let's power through this problem together! We have two scenarios to work with:
Scenario 1:
- Consumption: 50 units
- Amount collected: Rs. 700
Scenario 2:
- Consumption: 100 units
- Amount collected: unknown
From the given information, we can determine that the variable charge per unit is Rs. 700/50 = Rs. 14.
Now, let's move on to the next scenario:
Scenario 3:
- Consumption: 200 units
- Amount collected: unknown
We are told that Scenario 3's bill amount is 5/4 times that of Scenario 2's bill amount. Thus, we can say:
(5/4) * [Amount collected in Scenario 2] = [Amount collected in Scenario 3]
Let's substitute the variable charge into Scenario 2:
(5/4) * [(100 units) * (variable charge per unit)] = [(200 units) * (variable charge per unit)]
Simplifying this equation, we get:
(5/4) * (100 units * Rs. 14) = (200 units * Rs. 14)
Now, we can solve for the amount collected in Scenario 2:
(5/4) * (100 units * Rs. 14) = (200 units * Rs. 14)
Simplifying further:
(5/4) * (1400 Rs.) = (2800 Rs.)
Thus, the amount collected in Scenario 2 is Rs. 2800.
Now, we can determine the fixed charge by subtracting the variable charge from the total amount collected:
Total amount collected in Scenario 2 (Rs. 2800) = Fixed charge + (100 units * Rs. 14)
We can rearrange this equation to solve for the fixed charge:
Fixed charge = Total amount collected in Scenario 2 - (100 units * Rs. 14)
Fixed charge = Rs. 2800 - Rs. 1400
Fixed charge = Rs. 1400
So, the fixed charge per month is Rs. 1400.
Remember, this calculation assumes a linear relationship between consumption and the variable charge. Now, let's hope the fixed charge doesn't cause any shocking reactions!
To find the fixed charge per month, we need to understand the relationship between the total bill amount and the number of units consumed. Let's break down the problem step by step:
1. Let's denote the fixed charge as "F" and the variable charge per unit as "V".
2. According to the given information, when the consumer used 50 units, the total bill amount was Rs. 700. We can write this as an equation: F + 50V = 700.
3. We are also told that when the consumption increased from 100 units to 200 units, the bill amount increased to 5/4 times the former. Mathematically, we can write this as an equation: F + 100V = (5/4) * (F + 50V).
4. Now, we have two equations with two variables (F and V). We can solve the system of equations to find their values.
To solve the system of equations, we can use the method of substitution:
Step 1: Solve the first equation for F in terms of V.
F = 700 - 50V
Step 2: Substitute the value of F in the second equation.
(700 - 50V) + 100V = (5/4) * (700 - 50V + 50V)
700 - 50V + 100V = (5/4) * 700
Step 3: Simplify the equation.
700 + 50V = (5/4) * 700
700 + 50V = 875
Step 4: Solve for V.
50V = 875 - 700
50V = 175
V = 175/50
V = 3.5
Step 5: Substitute the value of V into the first equation to find F.
F + 50(3.5) = 700
F + 175 = 700
F = 700 - 175
F = 525
Therefore, the fixed charge per month is Rs. 525.
Clearly, the fixed charge is always 700.
You must want the variable charge per unit. That means you want to solve
700+200x = 5/4(700+100x)
unless something else has been garbled.