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
You're on a roll — Step 1: Define variables and set up the system of linear equations. Let g be the cost of one geometrical set. Let m be the cost of one mathematical table. From the problem statement, we have two equations: 1) Five geometrical sets and three mathematical tables cost sh. 2,816: 5g + 3m = 2816 2) Three geometrical sets and five mathematical tables cost sh. 3,360: 3g + 5m = 3360 Step 2: Write the system of equations in matrix form AX = B. 5 & 3 \\ 3 & 5 g \\ m = 2816 \\ 3360 Here, A = 5 & 3 \\ 3 & 5 , X = g \\ m , and B = 2816 \\ 3360 . Step 3: Find the determinant of matrix A. (A) = (5 × 5) - (3 × 3) = 25 - 9 = 16 Step 4: Find the inverse of matrix A, denoted as A^-1. For a 2 × 2 matrix a & b \\ c & d , the inverse is (1)/((A)) d & -b \\ -c & a . A^-1 = (1)/(16) 5 & -3 \\ -3 & 5 Step 5: Solve for X using X = A^-1B. g \\ m = (1)/(16) 5 & -3 \\ -3 & 5 2816 \\ 3360 Perform the matrix multiplication: g \\ m = (1)/(16) (5 × 2816) + (-3 × 3360) \\ (-3 × 2816) + (5 × 3360) g \\ m = (1)/(16) 14080 - 10080 \\ -8448 + 16800 g \\ m = (1)/(16) 4000 \\ 8352 Step 6: Divide by the determinant to find the values of g and m. g = (4000)/(16) = 250 m = (8352)/(16) = 522 The cost of one geometrical set is sh. 250. The cost of one mathematical table is sh. 522. The final answer is Cost of one geometrical set = sh. 250, Cost of one mathematical table = sh. 522. Got more? Send 'em!