7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an equation that represents the cost of renting the party room in terms of the number of people attending the party.

C = 6.75n + 50

Step-by-step explanation:

The equation for the cost of renting the party room can be written in the form;

C = mn+k ... i

Where C = cost

n = number of people

Substituting the 2 cases into the equation we have,

Case 1

117.5 = 10m + k ... 1

Case 2

151.25 = 15m + k ... 2

Subtracting eqn 1 from 2 we have

151.25 - 117.50 = 15m - 10m

5m = 33.75

m = 33.75/5 = 6.75

Substituting m = 6.75 into eqn 1, we have

117.50 = 10 (6.75) + k

k = 117.5 - 67.50

k = 50

Therefore, rewriting the eqn i, we have

C = 6.75n + 50