The cost of a car service is partly constant and partly varies with the time it takes to do the work.it cost 9400 naira for a 5.5 hours service and 8200 naira for a 4 hours service.find the formula connecting cost,naira c with time T hours.and find the cost of a 7.5 services.
Let's assume that the constant part of the cost is represented by C naira and the variable part is represented by V naira per hour. We can use this information to set up two equations:
For the 5.5 hours service:
C + 5.5V = 9400
For the 4 hours service:
C + 4V = 8200
To find the formula connecting cost (C) with time (T) hours, we need to solve these equations simultaneously. First, let's solve for C in terms of V in both equations.
From the first equation:
C = 9400 - 5.5V
From the second equation:
C = 8200 - 4V
Since both equations equal C, we can set them equal to each other to get:
9400 - 5.5V = 8200 - 4V
Now, let's solve for V:
9400 - 8200 = 5.5V - 4V
1200 = 1.5V
V = 1200/1.5
V = 800
Now that we have the value of V, we can substitute it back into either of the original equations to solve for C. Let's use the first equation:
C + 5.5V = 9400
C + 5.5(800) = 9400
C + 4400 = 9400
C = 9400 - 4400
C = 5000
Therefore, the formula connecting cost (C) with time (T) hours is:
C = 5000 + 800T
To find the cost of a 7.5-hour service, we can plug T = 7.5 into the formula:
C = 5000 + 800(7.5)
C = 5000 + 6000
C = 11000
The cost of a 7.5-hour service is 11,000 naira.
To find the formula connecting cost (c) with time (T) in hours, we can use the information given:
We are told that the cost of a 5.5-hour service is 9400 naira, and the cost of a 4-hour service is 8200 naira.
Let's start by finding the constant component of the cost. We can subtract the variable cost from the total cost to get the constant cost.
For the 5.5-hour service:
Constant cost = Total cost - Variable cost
Constant cost = 9400 naira - (Variable rate * 5.5 hours)
For the 4-hour service:
Constant cost = 8200 naira - (Variable rate * 4 hours)
Now, we can set up two equations using the above information:
1. Constant Cost1 = 9400 naira - (Variable rate * 5.5 hours)
2. Constant Cost2 = 8200 naira - (Variable rate * 4 hours)
To find the variable rate, subtract equation 2 from equation 1:
Constant Cost1 - Constant Cost2 = (9400 naira - 8200 naira) - (Variable rate * (5.5 hours - 4 hours))
1200 naira = Variable rate * 1.5 hours
Divide both sides by 1.5 hours to solve for the variable rate:
Variable rate = 1200 naira / 1.5 hours
Variable rate = 800 naira/hour
Now that we have found the variable rate, we can substitute it into either equation 1 or equation 2 to solve for the constant cost. Let's use equation 1:
Constant Cost1 = 9400 naira - (800 naira/hour * 5.5 hours)
Constant Cost1 = 9400 naira - 4400 naira
Constant Cost1 = 5000 naira
Now we have the formula connecting the cost (c) with time (T):
c = Constant Cost + (Variable rate * T)
c = 5000 naira + (800 naira/hour * T)
To find the cost of a 7.5-hour service, substitute T = 7.5 into the formula:
c = 5000 naira + (800 naira/hour * 7.5 hours)
c = 5000 naira + 6000 naira
c = 11000 naira
Therefore, the cost of a 7.5-hour service is 11,000 naira.