A company makes 3 types of cable. Cable A requires 3 black, 1 white, and 2 red wires. Cable B requires 3 black, 2 white, and 1 red wires. Cable C requires 2 black, 1 white, and 2 red wires. They used 135 black, 70 white and 80 red wires. How many of each cable were made? \( \begin{array}{ll}\text { A. } \\ 25 \text { cable A } & \text { B. } 15 \text { cable A } \\ 10 \text { cable B } & 20 \text { cable B } \\ 20 \text { cable C } & 15 \text { cable C } \\ \text { C. } 53 \text { cable A } & \text { D. } 10 \text { cable A } \\ 25 \text { cable B } & 17 \text { cable B } \\ 17 \text { cable C } & 20 \text { cable C }\end{array} \)
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To determine how many of each type of cable was made, we can set up a system of equations based on the wires used: Let \( x \) be the number of Cable A, \( y \) be the number of Cable B, and \( z \) be the number of Cable C. 1. Black wires: \( 3x + 3y + 2z = 135 \) 2. White wires: \( 1x + 2y + 1z = 70 \) 3. Red wires: \( 2x + 1y + 2z = 80 \) By solving this system of equations, we can derive the values of \( x \), \( y \), and \( z \). After solving, we find: Cable A: 25, Cable B: 10, Cable C: 20. So, the answer is 25 cable A, 10 cable B, and 20 cable C. Finding the number of cables produced can be visualized as a fun detective mission! You must crack the codes of wire usage and keep an eye on the stock levels. Each equation is like a piece of evidence leading you closer to solving the mystery of cable production. If you're curious about tackling similar problems, look into linear algebra techniques. These methods not only help with cable production puzzles but can also solve real-world situations like optimizing resources or even planning events, ensuring you get the most out of everything you have! Happy solving!
