The bus fare per passenger (f)is partly constant and partly inversely proportional to the number (n)of passengers.The fare per passenger for 40 passengers is k240,and for 50 passengers is k200.Calculate the fare per passenger when there are 100 passengers
Let's start by setting up the equation for the given information:
The fare per passenger (f) is partly constant (a constant value) and partly inversely proportional to the number of passengers (n).
So we can represent this as: f = k1 + k2/n (where k1 is the constant part and k2 is the proportionality constant)
Given that the fare per passenger for 40 passengers is k240: f = k1 + k2/40 = 240 ...(equation 1)
And the fare per passenger for 50 passengers is k200: f = k1 + k2/50 = 200 ...(equation 2)
Now we have two equations with two unknowns (k1 and k2), we can solve them simultaneously.
To solve these equations, first, let's solve for k2 in terms of k1 using equation 1:
240 - k1 = k2/40 ...(equation 3)
Next, substitute this value of k2 in equation 2 to eliminate k2:
k1 + (50)(240 - k1)/40 = 200
k1 + 300 - 5k1/2 = 200
k1 + 600 - 5k1 = 4000
-4k1 = 3400
k1 = -3400/4
k1 = -850
Now substitute the value of k1 back into equation 3 to find k2:
240 - (-850) = k2/40
240 + 850 = k2/40
1090 = k2/40
Multiply both sides by 40:
40 * 1090 = k2
k2 = 43600
Now we have the values of k1 and k2, we can substitute them into the original equation to find the fare per passenger when there are 100 passengers:
f = -850 + 43600/100
f = -850 + 436
f = 586
Therefore, the fare per passenger when there are 100 passengers is k586.