25 tickets must be purchased in order for the total cost at Carnival M and Carnival P to be the same.
Given that,
Carnival M charges an entrance fee of $5.00 and $0.65 per ticket for the rides.
Carnival P charges an entrance fee of $10.00 and $0.45 per ticket for the rides.
We have to determine,
How many tickets must be purchased in order for the total cost at Carnival M and Carnival P to be the same?
According to the question,
Let, x be the number of tickets sold.
Carnival M charges $0.65 per ticket (0.65x) plus the entrance fee (5),
Carnival P charges $0.45 per ticket (0.45x) plus the entrance fee (10).
The price is the same for both carnivals, so set them equal to each other:
\(0.65x + 5 = 0.45x + 10\\\\0.65x + 5 = 0.45x + 10\\\\0.65x + 5 - 5 = 0.45x + 10 - 5\\\\0.65x -0.45x = 0.45x - 0.45x + 5\\\\\dfrac{0.2x}{0.2 }= \dfrac{5}{0.2}\\\\x = 25\)
Hence, 25 tickets must be purchased in order for the total cost at Carnival M and Carnival P to be the same.
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