Problem 1 · AMC 8 Stretch
Core
Arithmetic & Operations
Logic & Word Problems
identifying-relevant-datatranslate-text-into-mathematics
A class from a town of 4,300 people takes a trip to a mountain 120 km away. The class has 500 dollars in its treasury. The whole trip cost 360 dollars. That 360 dollars paid for the bus (110 dollars) plus a rope-walk activity that costs the same amount for each of the 25 students. (a) How much did the rope-walk cost for one student? (b) Which numbers in the problem were NOT needed to answer part (a)?
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Answer: 10 dollars per student; population, distance, and treasury are not needed
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Hint 1 of 3
Before you compute, sort the numbers into two piles: ones that change the rope-walk price per student, and ones that are just background story.
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Hint 2 of 3
The 360 dollars total is made of two things: the one bus fee (110 dollars) plus the rope-walk paid once for each of the 25 students.
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Hint 3 of 3
Subtract the bus fee from the total to get just the rope-walk money. Then split that evenly among the 25 students.
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Approach: Strip the irrelevant data, then subtract and divide
- The 360 dollars is the bus fee plus all the rope-walk fees. Take out the bus fee first: \(360 - 110 = 250\) dollars.
- That 250 dollars is shared equally by 25 students, so each student's rope-walk costs \(250 \div 25 = 10\) dollars.
- (a) The rope-walk costs 10 dollars per student.
- (b) The town's population (4,300), the distance (120 km), and the 500-dollar treasury are never used — they are background story, not needed for part (a).
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