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Vendor with fruit baskets
A vendor has to make fruit baskets using apples and bananas. The ratio of the number of apples to the number of bananas is the same in each fruit basket.
What is the maximum number of baskets that can be made using 35 apples and 125 bananas?
Show answer & explanation
The maximum number of identical fruit baskets is GCD(35, 125) = 5 baskets, each containing 7 apples and 25 bananas.
Step-by-step Derivation:
Step 1: For each basket to have identical counts of apples and bananas, the number of baskets must divide both 35 and 125.
Step 2: GCD(35, 125) = GCD(35, 20) = GCD(15, 20) = 5.
Step 3: Thus, 5 baskets can be made (each with 7 apples and 25 bananas).