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: Define variables for the cost prices. Let C_S be the cost price of the suit. Let C_H be the cost price of the shirt. Step 2: Formulate equations based on the first scenario. In the first scenario, the total selling price is GH¢14,800. The profit on the suit is 20%, so its selling price is C_S + 0.20 C_S = 1.20 C_S. The profit on the shirt is 10%, so its selling price is C_H + 0.10 C_H = 1.10 C_H. This gives us the first equation: 1.20 C_S + 1.10 C_H = 14800 (1) Step 3: Formulate equations based on the second scenario. In the second scenario, the total selling price is GH¢15,100. If the profit on the suit were 10%, its selling price would be C_S + 0.10 C_S = 1.10 C_S. If the profit on the shirt were 20%, its selling price would be C_H + 0.20 C_H = 1.20 C_H. This gives us the second equation: 1.10 C_S + 1.20 C_H = 15100 (2) Step 4: Solve the system of linear equations. We have the system: 1) 1.2 C_S + 1.1 C_H = 14800 2) 1.1 C_S + 1.2 C_H = 15100 Multiply equation (1) by 1.2 and equation (2) by 1.1 to eliminate C_H: 1.2 × (1.2 C_S + 1.1 C_H) = 1.2 × 14800 1.44 C_S + 1.32 C_H = 17760 (3) 1.1 × (1.1 C_S + 1.2 C_H) = 1.1 × 15100 1.21 C_S + 1.32 C_H = 16610 (4) Subtract equation (4) from equation (3): (1.44 C_S + 1.32 C_H) - (1.21 C_S + 1.32 C_H) = 17760 - 16610 0.23 C_S = 1150 C_S = (1150)/(0.23) = 5000 Step 5: Substitute the value of C_S into one of the original equations to find C_H. Using equation (1): 1.2(5000) + 1.1 C_H = 14800 6000 + 1.1 C_H = 14800 1.1 C_H = 14800 - 6000 1.1 C_H = 8800 C_H = (8800)/(1.1) = 8000 The cost price of the suit is GH¢5000. The cost price of the shirt is GH¢8000. The cost price of the suit is GH¢5000. The cost price of the shirt is GH¢8000. 3 done, 2 left today. You're making progress.