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
Step 1: Formulate the system of linear equations. Let k be the cost of one keyboard and c be the cost of one charger. From the first statement: "Three computer key boards and 2 charger cost Kshs. 5,100" 3k + 2c = 5100 (1) From the second statement: "4 similar keyboards and 3 similar chargers cost Kshs. 7,050" 4k + 3c = 7050 (2) Step 2: Express the system of equations in matrix form AX = B. A = 3 & 2 \\ 4 & 3 , X = k \\ c , B = 5100 \\ 7050 So, the matrix equation is: 3 & 2 \\ 4 & 3 k \\ c = 5100 \\ 7050 Step 3: Find the inverse of matrix A. The determinant of A is (A) = (3)(3) - (2)(4) = 9 - 8 = 1. The inverse of a 2 × 2 matrix a & b \\ c & d is (1)/(ad - bc) d & -b \\ -c & a . A^-1 = (1)/(1) 3 & -2 \\ -4 & 3 = 3 & -2 \\ -4 & 3 Step 4: Solve for X by multiplying A^-1 by B. X = A^-1B k \\ c = 3 & -2 \\ -4 & 3 5100 \\ 7050 Perform the matrix multiplication: k = (3)(5100) + (-2)(7050) k = 15300 - 14100 k = 1200 c = (-4)(5100) + (3)(7050) c = -20400 + 21150 c = 750 The cost of each keyboard is Kshs. 1200 and the cost of each charger is Kshs. 750. Cost of keyboard = Kshs. 1200, Cost of charger = Kshs. 750 That's 2 down. 3 left today — send the next one.