{"database": "grpo-one-example", "table": "results", "rows": [[14, "dsr-one-example-grpo_global_step_50", "gsm8k_main(0)", "13", "Question: Melanie is a door-to-door saleswoman. She sold a third of her vacuum cleaners at the green house, 2 more to the red house, and half of what was left at the orange house. If Melanie has 5 vacuum cleaners left, how many did she start with?\nAnswer:", "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nOutput format: end your response with \\boxed{<answer>} where <answer> is the final answer.\n\nQuestion: Melanie is a door-to-door saleswoman. She sold a third of her vacuum cleaners at the green house, 2 more to the red house, and half of what was left at the orange house. If Melanie has 5 vacuum cleaners left, how many did she start with?\nAnswer:<|im_end|>\n<|im_start|>assistant\n", "18", 1, "[18]", "[stop:-]", "To solve this problem, we need to work backwards from the information given. Let's denote the total number of vacuum cleaners Melanie started with as \\( x \\).\n\n1. After selling a third of her vacuum cleaners at the green house, she has \\( \\frac{2}{3}x \\) left.\n2. Then, she sold 2 more to the red house, so she has \\( \\frac{2}{3}x - 2 \\) left.\n3. After selling half of what was left at the orange house, she has \\( \\frac{1}{2} \\left( \\frac{2}{3}x - 2 \\right) \\) left.\n4. We know that after these sales, she has 5 vacuum cleaners left, so we can set up the equation:\n   \\[\n   \\frac{1}{2} \\left( \\frac{2}{3}x - 2 \\right) = 5\n   \\]\n\nNow, let's solve this equation step by step.\n\nFirst, multiply both sides by 2 to clear the fraction:\n\\[\n\\frac{2}{3}x - 2 = 10\n\\]\n\nNext, add 2 to both sides to isolate the term with \\( x \\):\n\\[\n\\frac{2}{3}x = 12\n\\]\n\nThen, multiply both sides by \\( \\frac{3}{2} \\) to solve for \\( x \\):\n\\[\nx = 18\n\\]\n\nSo, Melanie started with 18 vacuum cleaners.\n\nThe final answer is \\(\\boxed{18}\\)."]], "columns": ["id", "model_name", "task_name", "sample_id", "prompt_actual", "prompt_full", "gold_answer", "is_correct", "extracted_answers", "stop_reasons", "response_1"], "primary_keys": ["id"], "primary_key_values": ["14"], "units": {}, "query_ms": 1.858722884207964}