This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for number 18. 18) Step 1: Find the greatest common divisor (G.C.D.) of the lengths of the three wires (30 m, 36 m, and 84 m). This will be the length of the longest possible equal pieces. Prime factorization of each length: 30 = 2 × 3 × 5 36 = 2^2 × 3^2 84 = 2^2 × 3 × 7 The common prime factors are 2 and 3. The lowest power of 2 is 2^1. The lowest power of 3 is 3^1. G.C.D. = 2^1 × 3^1 = 2 × 3 = 6 So, each piece of wire will be 6 meters long. Step 2: Calculate the number of pieces obtained from each wire. Number of pieces from the 30 m wire = (30)/(6) = 5 pieces Number of pieces from the 36 m wire = (36)/(6) = 6 pieces Number of pieces from the 84 m wire = (84)/(6) = 14 pieces Step 3: Calculate the total least number of pieces. Total pieces = 5 + 6 + 14 = 25 pieces 25 pieces That's 2 down. 3 left today — send the next one.