Answer:
Arthur should select the Mount Joy Pool when there are less than 10 people at the party
Explanation:
The initial fee to rent the Woodbridge Pool = $50
The additional fee per person after renting = $5
The initial fee to rent at Mount Joy Pool = 0 (no initial fee)
The fee per person at Mount Joy Pool = $10
The equation of a straight line is y = m·x + c
Ley y represent the total cost of renting the pool, x, represent the number of persons in the pool, m represent the fee per person and c represent the initial charges, we get;
The total cost of renting Woodbridge Pool, y = 5·x + 50
The total cost of renting the Joy Pool, y = 10·x
Equating both values of y gives;
5·x + 50 = 10·x
∴ 5·x = 50
x = 50/5 = 10
x = 10
From the above equations, the cost of renting the pool is lower for the Joy Pool when there are less than 10 persons at the pool
It will cost the same amount to rent the pool when the number of persons in the pool are 10 persons and the cost of renting the Mount Joy Pool will be more than the cost of renting the Woodbridge Pool, when there are more than 10 persons
Therefore, Arthur should select the Mount Joy Pool when there are less than 10 people at the party.