the charge for telephone call ,t,partly constant and partly varies with the number n of call. the bill for 420 units of call is 806,while the bill for 200units is 410
A)calculate the charge for 460 unit of electricity
B)find a formula for T
so t = nk + c, where n is the number of calls
your given information yields the following pair of equations:
806 = 420k + c
410 = 200k + c
subtract them:
396 = 220k
k = 9/5 = 1.8
sub into 410 = 200k + c ---> c = .....
and you got your equation. B)
plug in n = 460, and evaluate t
That's great
A) As the bill is partly constant and partly varies with the number of calls, let's calculate the difference between the two bills for 420 units and 200 units:
Difference in charge = 806 - 410 = 396
Now, let's calculate the difference per unit:
Difference per unit = 396 / (420 - 200) = 396 / 220 = 1.8
To find the charge for 460 units, we can use the formula:
Charge = Bill for 200 units + (Difference per unit * Number of extra units)
Charge = 410 + (1.8 * 260)
Charge = 410 + 468 = 878
Therefore, the charge for 460 units of electricity would be 878.
B) To find a formula for T, we have constant part and variable part. Let's call the constant part K and the variable part V. We'll use the given information to find the values for K and V.
Given the bill for 420 units is 806:
K + V * 420 = 806 (Equation 1)
Given the bill for 200 units is 410:
K + V * 200 = 410 (Equation 2)
To find the formula for T, we need to solve these two equations simultaneously. Subtract Equation 2 from Equation 1:
(V * 420) - (V * 200) = 806 - 410
V * 220 = 396
V = 396 / 220
V = 1.8
Substitute the value of V back into either Equation 1 or 2 to find K:
K + 1.8 * 200 = 410
K + 360 = 410
K = 410 - 360
K = 50
Therefore, the formula for T is:
T = 50 + 1.8n
To solve this problem, we need to first determine the constant part and the varying part of the charge. Then we can use this information to calculate the charge for a different number of units and find the formula for T.
Step 1: Determining the Constant and Varying Parts
Let the constant part of the charge be represented by 'c' and the varying part be represented by 'v'. We can express the total charge, 't', as the sum of the constant part and the varying part: t = c + vn.
We are given two sets of data:
1) When the number of units is 420, the total charge is 806.
2) When the number of units is 200, the total charge is 410.
Using these values, we can set up the following equations:
Equation 1: 806 = c + 420v
Equation 2: 410 = c + 200v
Now, let's solve these equations simultaneously to find the values of 'c' and 'v'.
Step 2: Solving the Equations
From Equation 2, we can subtract c from both sides to isolate 'v':
200v = 410 - c
Next, rearrange Equation 1 to solve for 'c':
c = 806 - 420v
Substitute the value of c from Equation 1 into Equation 2:
200v = 410 - (806 - 420v)
200v = 410 - 806 + 420v
-220v = -396
v = (-396) / (-220)
v = 1.8
Now, substitute the value of 'v' back into Equation 1 to find the value of 'c':
806 = c + (420 * 1.8)
806 = c + 756
c = 806 - 756
c = 50
So, the constant part 'c' is 50 and the varying part 'v' is 1.8.
Step 3: Calculating the Charge for 460 Units
Using the formula t = c + vn, plug in the known values:
t = 50 + (460 * 1.8)
t = 50 + 828
t = 878
Therefore, the charge for 460 units of call is 878.
Step 4: Finding the Formula for T
Based on the calculations, the formula for 't' in terms of 'n' is:
T = 50 + 1.8n
So, the formula for T is T = 50 + 1.8n.