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
To find the total number of cashiers, attendants, and mechanics for each location, we can use matrix multiplication. Step 1: Define the matrices. Let matrix P represent the number of personnel per type of filling station: P = 4 & 2 & 1 \\ 12 & 6 & 3 \\ 6 & 4 & 2 The rows represent Cashier, Attendant, and Mechanics, respectively. The columns represent Large, Medium, and Small stations. Let matrix S represent the number of filling stations of each type in Ebony and Imo: S = 3 & 7 \\ 5 & 8 \\ 12 & 4 The rows represent Large, Medium, and Small stations, respectively. The columns represent Ebony and Imo locations. Step 2: Multiply matrix P by matrix S. The product R = P × S will give the total number of personnel for each category in each location. R = 4 & 2 & 1 \\ 12 & 6 & 3 \\ 6 & 4 & 2 3 & 7 \\ 5 & 8 \\ 12 & 4 Step 3: Calculate the elements of the resulting matrix R. For Cashiers (Row 1 of R): • Ebony: (4 × 3) + (2 × 5) + (1 × 12) = 12 + 10 + 12 = 34 • Imo: (4 × 7) + (2 × 8) + (1 × 4) = 28 + 16 + 4 = 48 For Attendants (Row 2 of R): • Ebony: (12 × 3) + (6 × 5) + (3 × 12) = 36 + 30 + 36 = 102 • Imo: (12 × 7) + (6 × 8) + (3 × 4) = 84 + 48 + 12 = 144 For Mechanics (Row 3 of R): • Ebony: (6 × 3) + (4 × 5) + (2 × 12) = 18 + 20 + 24 = 62 • Imo: (6 × 7) + (4 × 8) + (2 × 4) = 42 + 32 + 8 = 82 Step 4: Form the final matrix R. R = 34 & 48 \\ 102 & 144 \\ 62 & 82 This matrix shows: • Row 1: Total Cashiers for Ebony (34) and Imo (48) • Row 2: Total Attendants for Ebony (102) and Imo (144) • Row 3: Total Mechanics for Ebony (62) and Imo (82) The total number of personnel for each location is: For Ebony: Cashiers: 34* Attendants: 102* Mechanics: 62* For Imo: Cashiers: 48* Attendants: 144* Mechanics: 82* That's 2 down. 3 left today — send the next one.