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SOLUTION TO BRAINTEASER NO. 7 DISCLAIMER This solution is but one of many possible methods for solving this problem. Various other solutions may lead to the same answers. This specific solution was provided by the Institute of Mathematical Sciences and Physics of the University of the Philippines Los Baños.
PROBLEM:
One of the receipts for a math tournament showed that 72 identical trophies were purchased for PhP _99.9_, where the first and last digits were illegible. How much did each trophy cost?
SOLUTION: Seeing as the purchase was made for 72 identical trophies, the total price should be divisible by 72, thus the total should also be divisible by both 8 and 9. For the price to be divisible by 8, the last three digits of the total cost should be divisible by 8. This condition is only possible if the last digit is 2. For the price to be divisible by 9, the first digit of the total cost should be 7. Thus, the total price is PhP 799.92. Divide that by 72 to get the price for each trophy.
ANSWER:
PhP 11.11
UNIVERSITY OF THE PHILIPPINES CIVIL ENGINEERING SOCIETY Department of Civil Engineering College of Engineering and Agro-industrial Technology University of the Philippines Los Baños
