results: 14

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id model_name task_name sample_id prompt_actual prompt_full gold_answer is_correct extracted_answers stop_reasons response_1
14 grpo-gsm8k-test-30ep-success_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? Answer: <|im_start|>system You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|> <|im_start|>user Output format: end your response with \boxed{<answer>} where <answer> is the final answer. 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? Answer:<|im_end|> <|im_start|>assistant 18 1 [18] [stop:-] To determine how many vacuum cleaners Melanie started with, we need to work backwards from the information given. Let's denote the total number of vacuum cleaners Melanie started with as \( x \). 1. After selling a third of her vacuum cleaners at the green house, she has \( \frac{2}{3}x \) vacuum cleaners left. 2. She then sold 2 more vacuum cleaners at the red house, so she has \( \frac{2}{3}x - 2 \) vacuum cleaners left. 3. After selling half of what was left at the orange house, she has \( \frac{1}{2} \left( \frac{2}{3}x - 2 \right) \) vacuum cleaners left, which is given to be 5. So, we can set up the equation: \[ \frac{1}{2} \left( \frac{2}{3}x - 2 \right) = 5 \] To solve for \( x \), we first eliminate the fraction by multiplying both sides of the equation by 2: \[ \frac{2}{3}x - 2 = 10 \] Next, we isolate the term involving \( x \) by adding 2 to both sides: \[ \frac{2}{3}x = 12 \] To solve for \( x \), we multiply both sides by \( \frac{3}{2} \): \[ x = 12 \times \frac{3}{2} = 18 \] Therefore, Melanie started with \(\boxed{18}\) vacuum cleaners.