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 the total number of oranges and calculate the share for the first boy. Let T be the total number of oranges. The first boy gets (1)/(3) of the total oranges. Oranges for the first boy = (1)/(3) T. Step 2: Calculate the remaining oranges after the first boy's share. Remaining oranges after the first boy = T - (1)/(3) T = (3)/(3) T - (1)/(3) T = (2)/(3) T. Step 3: Calculate the share for the second boy. The second boy gets (2)/(3) of the remainder from Step 2. Oranges for the second boy = (2)/(3) × ((2)/(3) T) = (4)/(9) T. Step 4: Calculate the remaining oranges after the second boy's share. Remaining oranges after the second boy = (2)/(3) T - (4)/(9) T. To subtract these fractions, find a common denominator, which is 9. (2)/(3) T = (2 × 3)/(3 × 3) T = (6)/(9) T. So, remaining oranges = (6)/(9) T - (4)/(9) T = (2)/(9) T. Step 5: Use the information about the last boy's share to find the total number of oranges. The last boy has 12 oranges, which is the final remainder calculated in Step 4. (2)/(9) T = 12 To solve for T, multiply both sides by (9)/(2): T = 12 × (9)/(2) T = (108)/(2) T = 54 The total number of oranges shared was 54. The total number of oranges shared was 54.