Samir and Ben are planning a day trip with their friends. Samir wants to go to a waterpark that charges $40 per person for admission, plus $5 per person for tube rentals. Ben wants to go to a rock-climbing gym that charges $150 to rent the facility, plus an additional $20 per person. Which equation can you use to find p, the number of people who would need to go on the trip for the two options to cost the same? Choices: (A)40p + 5p = 150 + 20p (B)40p + 5 = 150 + 20p How many people would need to go on the trip for the two options to cost the same? ____ people

Question

Samir and Ben are planning a day trip with their friends. Samir wants to go to a waterpark that charges $40 per person for admission, plus $5 per person for tube rentals. Ben wants to go to a rock-climbing gym that charges $150 to rent the facility, plus an additional $20 per person. Which equation can you use to find p, the number of people who would need to go on the trip for the two options to cost the same?   Choices: (A)40p + 5p = 150 + 20p (B)40p + 5 = 150 + 20p  How many people would need to go on the trip for the two options to cost the same?   ____ people

Bytelearn · Accepted Answer

Set Total Cost Equation: To find the correct equation, we need to set the total cost for the waterpark equal to the total cost for the rock-climbing gym. The total cost for the waterpark is the cost per person ($40) plus the cost for tube rentals ($5) multiplied by the number of people (p). The total cost for the rock-climbing gym is the flat facility rental fee ($150) plus the cost per person ($20) multiplied by the number of people (p).Calculate Total Cost Equations: The equation representing the total cost for the waterpark is 40p + 5p, where p is the number of people. The equation representing the total cost for the rock-climbing gym is 150 + 20p. To find the number of people for which the costs are the same, we set these two expressions equal to each other.Simplify Equations: The correct equation to find the number of people (p) for which the costs are the same is: 40p + 5p = 150 + 20p This simplifies to: 45p = 150 + 20pIsolate Variable: To solve for p, we need to isolate the variable on one side of the equation. We can do this by subtracting 20p from both sides of the equation: 45p - 20p = 150 This simplifies to: 25p = 150Solve for Number of People: Now, we divide both sides of the equation by 25 to solve for p: 25p / 25 = 150 / 25 This simplifies to: p = 6

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