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
Hey — ready when you are. a) Let x be the weight of a lemon in grams. Let y be the weight of an orange in grams. From the first statement, "3 lemons and 2 oranges weigh 200 grams": 3x + 2y = 200 From the second statement, "4 lemons and 4 oranges weigh 300 grams": 4x + 4y = 300 The two mathematical equations are: 3x + 2y &= 200 \\ 4x + 4y &= 300 b) Step 1: Write down the system of equations. 3x + 2y = 200 (1) 4x + 4y = 300 (2) Step 2: Simplify equation (2) by dividing by 2. (4x)/(2) + (4y)/(2) = (300)/(2) 2x + 2y = 150 (3) Step 3: Subtract equation (3) from equation (1) to eliminate y. (3x + 2y) - (2x + 2y) = 200 - 150 3x - 2x + 2y - 2y = 50 x = 50 Step 4: Substitute the value of x into equation (3) to find y. 2(50) + 2y = 150 100 + 2y = 150 2y = 150 - 100 2y = 50 y = (50)/(2) y = 25 The weight of a lemon is 50 grams and the weight of an orange is 25 grams. Lemon: 50 grams, Orange: 25 grams Send me the next one 📸