The charge for electricity consumption (E) is partly constant and partly varies as the number of (N) units used. The charge for 163 units is #453.8 while the charge for 42 units is #139.20. Calculate the charge per unit of electricity and obtain a formulae for E in terms of N

E(n) = xN + c

453.8 = 163N + c
139.2 = 42N + c
subtract them:
314.6 = 121N
N = 2.6

sub into 139.2 = 42N + c to find c

rewrite
E(n) = xN + c , replacing N and c with what we found

Finish the solving

Solve and obtain the formula for E in terms of N ( b) calculate the charge per unit of electricity

Finish the solving

Ah, electricity bills, the real-life horror movie. Let's see if we can shed some light on this calculation while keeping the mood a bit brighter, shall we?

First, let's find the constant part of the charge. We have data for two different unit amounts and their corresponding charges, so we can set up two equations:

163 units = 453.8 #
42 units = 139.20 #

Now, let's do some math magic!

453.8 - 139.20 = 314.60 #
163 - 42 = 121 units

So, it seems like 314.60 # is the variable charge for 121 units, which means the constant part of the charge should be:

453.8 - 314.60 = 139.20 #

Since the variable charge per unit remains the same, we can calculate it by dividing the variable charge by the number of units:

314.60 # / 121 units = 2.60 #

So, apparently, the charge per unit of electricity is 2.60 #.

Now, for the thrilling moment – the formula for E in terms of N:

E = C + V
E = C + (N × U)

where:
E: charge for electricity consumption
C: constant part of the charge
V: variable part of the charge
N: number of units used
U: charge per unit

Substituting the values we found earlier:

E = 139.20 # + (N × 2.60 #)

And voila! There's your electrifying formula for E in terms of N.

To calculate the charge per unit of electricity, we need to find the difference in charges for different units and then divide it by the difference in units consumed.

First, let's determine the constant part of the charge. We can do this by subtracting the variable part from the total charge for a given number of units.

For 163 units:
Charge for 163 units = #453.8
Variable part of the charge = Charge for 163 units - Charge for 42 units
Variable part = #453.8 - #139.20 = #314.60

Next, let's calculate the charge per unit of electricity:
Charge per unit of electricity = Variable part / (163 units - 42 units)
Charge per unit of electricity = #314.60 / 121 units
Charge per unit of electricity ≈ #2.60

Now that we have the charge per unit of electricity, we can obtain a formula for E in terms of N.

Formula for E:
E = Constant part + (Charge per unit of electricity) * N

Using the values we calculated earlier:
E = #314.60 + (#2.60 * N)
E = #2.60N + #314.60

So, the formula for E in terms of N is E = #2.60N + #314.60.