In a restaurant the cost of providing a particular type of food is partly constant and partly varies inversely to the number of People. If cost per head for 100 People is €30 and the cost for 40 People is €60 find the cost for 50 People
Let C be the constant cost, and V be the variable cost per person.
From the problem, we know that C + V(100) = 30*100 = 3000 (equation 1)
And C + V(40) = 60*40 = 2400 (equation 2)
Subtracting equation 2 from equation 1, we have:
C + V(100) - C - V(40) = 3000 - 2400
V(100) - V(40) = 600
Dividing both sides by 60, we get:
V(100/60) - V(40/60) = 600/60
V(5/3) - V(2/3) = 10
Subtracting V(2/3) from both sides, we have:
V(5/3) - V(2/3) - V(2/3) = 10 - V(2/3)
V(5/3) = 10 - V(2/3)
Multiplying both sides by 3/5, we get:
V = (3/5)(10 - V(2/3))
V = 6 - (3/5)V(2/3)
V = 6 - V(2/5)
Multiplying both sides by 5, we get:
5V = 30 - 2V
Adding 2V to both sides, we have:
7V = 30
Dividing both sides by 7, we get:
V = 30/7
For 50 people, the cost would be C + V(50) = C + (30/7)(50)
So the cost for 50 people would be C + (30/7)(50). Answer: \boxed{C + \frac{1500}{7}}.