The number of tickets that should be purchased for the cost of both carnival to be equal is 10 tickets.
Assume the number of tickets to be purchased is x.
The expression for the total cost at Carnival M is:
= Entrance fee + (price of tickets x number of tickets)
= 5 + 0.50x
The expression for the total cost at Carnival P is:
= 7 + 0.30x
To find the number of tickers, equate both expressions:
5 + 0.50x = 7 + 0.30x
0.50x - 0.30x = 7 - 5
0.20x = 2
x = 2 / 0.20
= 10 tickets
10 tickets will need to be bought to both Carnivals for the cost to be the same.
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