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.

Answer 1

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