The cost of a car service is partly constant and partly varies with the time it takes to do the work .if cost 3500 naria for a 5 1/2 hour service and 2900 naira for a 4 hour service. Find the formula connecting cost , naira C with time ,T hours, hence find the cost of a 7 1/2 hour service.
Let the constant cost be C0 and the variable cost per hour be C1. We can use the information given to form two equations and solve for C0 and C1:
From the first service: 3500 = C0 + 5.5C1
From the second service: 2900 = C0 + 4C1
Subtracting the second equation from the first gives:
600 = 1.5C1
C1 = 400
Substituting back into either equation gives:
C0 = 1300
Therefore, the formula for cost, C, in terms of time, T, is:
C = 1300 + 400T
To find the cost of a 7 1/2 hour service, we simply substitute T = 7.5 into the formula:
C = 1300 + 400(7.5) = 4300 naira
Therefore, the cost of a 7 1/2 hour service is 4300 naira.
To find the formula connecting cost and time, we can use the given information of two data points.
Let's denote C as the cost in naira and T as the time in hours.
From the given data:
For a 5 1/2 hour service, cost (C) = 3500 naira
For a 4-hour service, cost (C) = 2900 naira
Let's find the constant cost and the rate of variation.
Step 1: Find the constant cost:
To find the constant cost, we need to subtract the variable cost from the total cost for a given time.
For a 5 1/2 hour service:
Constant cost (CC) = Total cost - Variable cost
CC = 3500 - Variable cost
For a 4-hour service:
CC = 2900 - Variable cost
Since the constant cost is the same in both cases, we can equate the two equations:
3500 - Variable cost = 2900 - Variable cost
Simplifying the equation, we find:
3500 = 2900
This means the constant cost (CC) is 3500 naira.
Step 2: Find the rate of variation:
The rate of variation will give us the cost per hour. We can find the rate of variation by dividing the difference in cost by the difference in time.
For a 5 1/2 hour service:
Rate of variation (RV) = (Total cost - Constant cost) / Time
RV = (3500 - 2900) / 5.5
For a 4-hour service:
RV = (2900 - 3500) / 4
Simplifying the equations:
RV = 600 / 5.5
RV = 109.09 naira/hour
RV = -600 / 4
RV = -150 naira/hour
The negative sign indicates a decrease in cost with an increase in time.
Step 3: Write the cost-time formula:
We now have the constant cost (CC) and the rate of variation (RV). The formula connecting cost (C) and time (T) is given by:
C = CC + RV * T
Substituting the values:
C = 3500 + 109.09 * T
To find the cost of a 7 1/2 hour service, we can substitute T = 7.5 into the formula:
C = 3500 + 109.09 * 7.5
C = 3500 + 818.18
C = 4318.18 naira
Therefore, the cost of a 7 1/2 hour service is 4318.18 naira.