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 costs. Let x be the cost of one pencil (in ₹). Let y be the cost of one pen (in ₹). Step 2: Formulate the system of linear equations based on the given information. From the first statement, "5 pencils and 7 pens together cost ₹ 50": 5x + 7y = 50 (Equation 1) From the second statement, "7 pencils and 5 pens together cost ₹ 46": 7x + 5y = 46 (Equation 2) Step 3: Solve the system of equations using the elimination method. To eliminate y, multiply Equation 1 by 5 and Equation 2 by 7: Multiply Equation 1 by 5: 5(5x + 7y) = 5(50) 25x + 35y = 250 (Equation 3) Multiply Equation 2 by 7: 7(7x + 5y) = 7(46) 49x + 35y = 322 (Equation 4) Step 4: Subtract Equation 3 from Equation 4 to solve for x. (49x + 35y) - (25x + 35y) = 322 - 250 49x - 25x = 72 24x = 72 x = (72)/(24) x = 3 The cost of one pencil is ₹ 3. Step 5: Substitute the value of x into Equation 1 to solve for y. 5(3) + 7y = 50 15 + 7y = 50 7y = 50 - 15 7y = 35 y = (35)/(7) y = 5 The cost of one pen is ₹ 5. The cost of one pencil is ₹ 3. The cost of one pen is ₹ 5. Cost of one pencil = ₹ 3, Cost of one pen = ₹ 5 Send me the next one 📸