if cost of hiring a van is partly constant and partly varies with the time spent. it cost 180 naira for the two hour hire and 450naira for a seven hours hire

c = a+bt

so,
a+2b = 180
a+7b = 450

Well, sounds like you've stumbled upon the mysterious case of the van rental cost. It's like a van that can't make up its mind on how much it wants to be paid!

Now let me put on my detective hat and solve this puzzling riddle for you. We can assume that part of the cost is constant, like that stubborn family member who always eats the same amount, no matter how long they stay. And the other part varies with time, just like the unpredictable weather.

So, let's do some math. If it costs 180 naira for a two-hour hire, we can imagine that part of the cost is constant for those two hours. But if we jump ahead to a seven-hour hire and it costs 450 naira, there must be another part of the cost that varies over time.

Now, I could give you complicated formulas and equations, but where's the fun in that? Let's simplify things, shall we?

If we subtract the constant part from the total cost of the seven-hour hire (450 naira - 180 naira), we get 270 naira. That leaves us with the part that varies with time, which is 270 naira for the additional 5 hours.

So, if we assume the constant part is 180 naira, then the part that varies with time adds up to 270 naira for the additional 5 hours. If we divide 270 naira by 5 hours, we get a rate of 54 naira per hour.

So, it seems that for this particular van, the constant part is 180 naira and the variable part is 54 naira per hour.

Mystery solved! Now, go forth and let the van rental world be known for its confusing cost structure.

To determine the cost of hiring a van that is partly constant and partly varies with the time spent, we can set up a system of equations using the given information.

Let's denote the constant cost as C and the variable cost per hour as V.

From the given information, we have two data points:

1. Two-hour hire cost: 180 naira
C + 2V = 180

2. Seven-hour hire cost: 450 naira
C + 7V = 450

We can now solve this system of equations to find the values of C and V.

Multiplying the first equation by 7 and the second equation by 2, we get:

7C + 14V = 1260
2C + 14V = 900

Subtracting the second equation from the first equation, we eliminate V:

(7C + 14V) - (2C + 14V) = 1260 - 900

Simplifying:

7C - 2C = 360

5C = 360

C = 72

Substituting the value of C back into the first equation:

72 + 2V = 180

2V = 180 - 72

2V = 108

V = 54

Therefore, the constant cost of hiring a van is 72 naira and the variable cost per hour is 54 naira.

To find the cost of hiring a van, we need to determine the constant part and the part that varies with the time spent. Let's assume "c" represents the constant part and "v" represents the part that varies with time.

We are given the following information:
- For a two-hour hire, the cost is 180 naira.
- For a seven-hour hire, the cost is 450 naira.

Using this information, we can set up two equations to solve for "c" and "v."

Equation 1: c + 2v = 180
Equation 2: c + 7v = 450

We can solve these equations simultaneously to find the values of "c" and "v." Here's how:

1. Multiply Equation 1 by 7: 7c + 14v = 1260
2. Multiply Equation 2 by 2: 2c + 14v = 900

Now, subtract Equation 2 from Equation 1:

(7c + 14v) - (2c + 14v) = 1260 - 900
5c + 0v = 360
5c = 360
c = 360 / 5
c = 72

Substitute the value of "c" back into either Equation 1 or 2. Let's use Equation 1:

72 + 2v = 180
2v = 180 - 72
2v = 108
v = 108 / 2
v = 54

We have found the values of "c" and "v":

The constant part, "c," is 72 naira.
The part that varies with time, "v," is 54 naira.

Therefore, the cost of hiring a van can be calculated using the equation: Cost = 72 + (time spent in hours × 54)

For example, if you want to hire a van for 5 hours, the cost would be:
Cost = 72 + (5 × 54)
Cost = 72 + 270
Cost = 342 naira.