2014/15 AHSMC Part 1 Problem 4

Problem 4 of 16

Chau and Matt are picking berries. On Monday Matt picks twice as many kilograms of berries as Chau does, and on Tuesday Chau picks twice as many kilograms of berries as Matt does. Between them, they pick a total of $30$ kilograms of berries over the two days. The number of kilograms of berries Chau picks over the two days is

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Solution

Let Chau pick $x$ kilograms of berries on Monday and Matt pick $y$ kilograms of berries on Tuesday. Then $3x + 3y = 30$ so that $x + y = 10$ . The number of kilograms Chau picks over the two days is $x + 2y$ . This expression can take on infinitely many values if all we know is that $x + y = 10$ . For example we may have $x = 0$ so that $y = 10$ and $x + 2y = 20$ ; or we may have $x = 4$ so that $y = 6$ and $x + 2y = 16$ ; and so on. The answer is (E).

University of Alberta

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