The charge for telephone calls T,is partly constant and partly varies with the number n of units of call.The bill for 580 units of call is #900, while the bill for 310 units is #500.a.obtain the charge per unit of call.b find a formula for T.
You know that T = kn+b
So, you just have to solve for k and b in
580k + b = 900
310k + b = 500
To solve this problem, we need to set up and solve a system of equations using the provided information.
Let's define the following variables:
C = constant charge
V = variable charge per unit of call
T = total charge for a given number of units
From the problem statement, we can derive the following equations:
For 580 units of call:
T = C + V * n
900 = C + V * 580 -- Equation 1
For 310 units of call:
T = C + V * n
500 = C + V * 310 -- Equation 2
Using these equations, we can now solve for C and V.
Step 1: Solve for C
Subtract Equation 2 from Equation 1 to eliminate the variable C:
900 - 500 = C + V * 580 - C - V * 310
400 = V * 580 - V * 310
400 = V * (580 - 310)
400 = V * 270
Therefore, V = 400/270
Step 2: Substitute V to solve for C
Substitute the value of V in Equation 1 or 2 to find C.
Using Equation 1: 900 = C + (400/270) * 580
C = 900 - (400/270) * 580
Now, we have the values of C and V:
C = 900 - (400/270) * 580
V = 400/270
To answer the specific questions:
a. Charge per unit of call:
The charge per unit of call is V, which is equal to 400/270 (approximately 1.481).
b. Formula for T:
The formula for T is T = (900 - (400/270) * n + (400/270) * n.
Note: The above calculations demonstrate a method to obtain the charge per unit of call and a formula for T based on the given information.