The cost of providing a plate of lunch to a certain group of people is partly constant and partly inversely proportional to the number of people. If it costs #30 per plate to feed 40 people,find the cost per plate to feed 50 people.
y(x) = a + b/x
a + b/40 = 30
40a+b = 1200
You need another equation to pin down a and b.
For example, you might have
a=20 and b=400
In that case,
y(x) = 20 + 400/x
y(50) = 20+400/50 = 28
Or, you might have
a=10 and b=800
Then
y(x) = 10 + 800/x
y(50) = 10+800/50 = 26
To find the cost per plate to feed 50 people, we need to determine the equation that relates the cost and the number of people, given the information provided.
Let's break down the problem step by step:
1. We are told that the cost of providing lunch is partly constant, which means there is a fixed cost involved, regardless of the number of people.
2. Additionally, the cost is partly inversely proportional to the number of people. In other words, as the number of people increases, the cost per plate decreases.
3. We are given that it costs #30 per plate to feed 40 people. This will help us determine the constant part of the cost equation.
Now, let's calculate the constant cost:
To find the constant cost, we can use the given information that it costs #30 per plate to feed 40 people. If the cost is constant, we can establish the equation:
Cost = Constant Cost + (Inverse Proportion)
Given: Cost = #30, Number of people = 40
So, we have:
#30 = Constant Cost + (Inverse Proportion) ----- (Equation 1)
Since the inverse proportion is inversely proportional to the number of people, we can express it as:
Inverse Proportion = K / Number of people
Here, K represents the constant of inverse proportionality.
So, Equation 1 becomes:
#30 = Constant Cost + (K / Number of people)
Now, let's substitute the given values (#30 and 40) into this equation to solve for the Constant Cost:
#30 = Constant Cost + (K / 40) ----- (Equation 2)
By rearranging Equation 2, we can find the constant cost:
Constant Cost = #30 - (K / 40) ----- (Equation 3)
Since we only need to find the constant cost, we don't need to know the value of K.
Now that we have the constant cost, we can find the cost per plate to feed 50 people.
Using a similar approach, we'll use the equation:
Cost = Constant Cost + (K / Number of people)
Let's substitute the values (#30, 50) into this equation and solve for the cost:
Cost = Constant Cost + (K / Number of people)
Cost = Constant Cost + (K / 50)
Now, substitute the value of the Constant Cost from Equation 3:
Cost = (#30 - (K / 40)) + (K / 50)
Simplifying the equation will give us the cost per plate to feed 50 people.