This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Let c be the cost price of one chair and t be the cost price of one table. Consider the following problem: A shopkeeper buys 2 chairs and 3 tables for a total cost of 180. He sells the chairs at a 20% profit and the tables at a 10% loss. If his total selling price for all items is 192, find the cost price of one chair and one table. Step 1: Set up the equation for the total cost. The total cost of 2 chairs and 3 tables is 180. 2c + 3t = 180 (*) Step 2: Set up the equation for the total selling price using profit and loss percentages. A 20% profit on a chair means its selling price is c + 0.20c = 1.20c. A 10% loss on a table means its selling price is t - 0.10t = 0.90t. The total selling price for 2 chairs and 3 tables is 192. 2(1.20c) + 3(0.90t) = 192 2.40c + 2.70t = 192 (**) Step 3: Solve the system of simultaneous equations. From equation (*), express c in terms of t: 2c = 180 - 3t c = 90 - (3)/(2)t Substitute this expression for c into equation (**): 2.40(90 - (3)/(2)t) + 2.70t = 192 216 - 3.6t + 2.7t = 192 216 - 0.9t = 192 0.9t = 216 - 192 0.9t = 24 t = (24)/(0.9) = (240)/(9) = (80)/(3) Now substitute the value of t back into the expression for c: c = 90 - (3)/(2)((80)/(3)) c = 90 - (80)/(2) c = 90 - 40 c = 50 The cost price of one chair is 50 and the cost price of one table is (80)/(3) (approximately 26.67). The cost price of one chair is \50 and the cost price of one table is \ (80)/(3). That's 2 down. 3 left today — send the next one.