The charge for telephone calls T is partly constant and partly varies with the number N of units of call. The bill for 420 units of call is 806 naira, while the bill for 200 units is 410 naira.Obtain the charge per unit of call, find a formula for T
m = charge per unit of call , b = fixed charge
T = m N + b
806 = m * 420 + b
410 = m * 200 + b
subtracting equations ... 396 = m * 220 ... m = 9/5 = 1.8
substitute back to find b
To find the charge per unit of call, we can solve a system of equations using the given information.
Let's assume the constant part of the charge is C and the variable part of the charge per unit is V.
From the given information, we can form two equations:
Equation 1: C + V(420) = 806
Equation 2: C + V(200) = 410
To solve this system of equations, we'll use the method of elimination.
Subtracting Equation 2 from Equation 1, we get:
(C + V(420)) - (C + V(200)) = 806 - 410
C + 420V - C - 200V = 396
220V = 396
V = 396/220
V = 1.8
Now, substitute the value of V into either of the original equations, let's use Equation 1:
C + (1.8)(420) = 806
C + 756 = 806
C = 806 - 756
C = 50
Therefore, the charge per unit of call is 1.8 naira, and the formula for T is:
T = 50 + 1.8N
To find the charge per unit of call, we can subtract the constant part of the charge from the total bill and then divide the result by the number of units of call.
Let's denote the constant charge as C and the charge per unit of call as U.
From the given information,
For 420 units of call, the bill is 806 naira. Therefore, we have the equation:
C + 420U = 806 .....(1)
For 200 units of call, the bill is 410 naira. Therefore, we have the equation:
C + 200U = 410 .....(2)
To solve these equations and find the values of C and U, we can use the method of substitution or elimination.
Let's use the method of elimination by subtracting equation (2) from equation (1):
(C + 420U) - (C + 200U) = 806 - 410
220U = 396
U = 396 / 220
U ≈ 1.8 naira (rounded to two decimal places)
Now that we have the value of U, we can substitute it back into either equation (1) or (2) to find the value of C.
Using equation (1):
C + 420U = 806
C + 420 * 1.8 = 806
C + 756 = 806
C = 806 - 756
C = 50 naira
Therefore, we now have the values of C and U:
C = 50 naira (constant charge)
U ≈ 1.8 naira (charge per unit of call)
To find the formula for T, we can substitute the values of C and U into the equation:
T = C + NU
T = 50 + 1.8N
So, the formula for T is T = 50 + 1.8N.