Question

The weekly cost per person to rent a cottage on a lake varies inversely with the number of people who share the cost. When four people share the cost, each one pays $312.

A) Write an equation relating the cost per person c and the number n of people who share the cost.

B) If six people share the cost instead of four, how much does the cost per person decrease?

Answer 1

A) When the relation is inverse, the product of the two related values is a constant. Here we have
n·c = 4·312
n·c = 1248 . . . . an equation relating n and c
You can rearrange this to
c = 1248/n


B) Using 6 for n, we have
c = 1248/6 = 208
The cost per person decreases from 312 to 208, so decreases by $104.