the monthly charge C of an electricity company is made up of follows:A constant charge a and A charge which varies directly as N the number of units used . when N=80 C =820 naira . When N =124 , C =1040 naira find the relationship between C and N ,find C when N = 180

c = a + n k

820 = a + 80 k
1040 = a + 124 k
-----------------subtract
-220 = -44 k

so k = 5
820 = a + 80*5 = a + 400
a = 420
so
c = 420 + 5 n

if n = 180
then
c = 420 + 80(180)
c = 420 + 14,400
c = 14,820

N♾C

N=KC
80=K(820)
K=80/820
K=4/41
The relationship (N=4/41C)

To find the relationship between C and N, we can use the given information and solve for the values of the constant charge "a" and the charge that varies directly with the number of units used.

Let's start by writing down the relationship between C and N:

C = a + bN

Where:
C is the monthly charge
N is the number of units used
a is the constant charge
b is the charge that varies directly with N.

Using the given values of N and C:
When N = 80, C = 820 naira
When N = 124, C = 1040 naira

Plugging in these values into the equation, we get two equations:

820 = a + b(80) (Equation 1)
1040 = a + b(124) (Equation 2)

Now, let's solve these equations to find the values of a and b.

First, let's rearrange Equation 1:

a + 80b = 820

Next, rearrange Equation 2:

a + 124b = 1040

Now, we will solve these two equations simultaneously to find the values of a and b.

Subtracting Equation 1 from Equation 2, we get:

(124b - 80b) = (1040 - 820)

44b = 220
b = 220/44
b = 5

Now, substitute the value of b into Equation 1:

a + 80(5) = 820
a + 400 = 820
a = 820 - 400
a = 420

So, we have found that a = 420 and b = 5.

Now we can write the relationship between C and N:

C = 420 + 5N

To find the monthly charge C when N = 180, substitute N = 180 into the equation:

C = 420 + 5(180)
C = 420 + 900
C = 1320

Therefore, when N = 180, the monthly charge C is 1320 naira.