Subjects algebra

Bead Necklaces

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Bead Necklaces


1. Let's denote the number of beads each girl started with as $x$ and $y$. Given that they used the same amount of beads to make their necklaces, this implies they took away the same number of beads from their starting amounts. 2. If both girls used $k$ beads to make their necklaces, the remaining beads for each girl are $x-k$ and $y-k$ respectively. 3. To analyze further, we need more information, such as how many beads each had originally, the amount used, or the resultant beads after making the necklace. 4. Without additional data or equations, we cannot solve for the exact amounts but can express their leftovers in terms of $x$, $y$, and $k$. So, the problem states the initial beads are different but the quantity used is the same: mathematically, $x \neq y$ and the beads used $k$ satisfy $k \leq \min(x,y)$.