results: 14

This data as json

id model_name task_name sample_id prompt_actual prompt_full gold_answer is_correct extracted_answers stop_reasons response_1
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? 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 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 \( x \). 1. After selling a third of her vacuum cleaners at the green house, she has \( \frac{2}{3}x \) left. 2. Then, she sold 2 more to the red house, so she has \( \frac{2}{3}x - 2 \) left. 3. After selling half of what was left at the orange house, she has \( \frac{1}{2} \left( \frac{2}{3}x - 2 \right) \) left. 4. We know that after these sales, she has 5 vacuum cleaners left, so we can set up the equation: \[ \frac{1}{2} \left( \frac{2}{3}x - 2 \right) = 5 \] Now, let's solve this equation step by step. First, multiply both sides by 2 to clear the fraction: \[ \frac{2}{3}x - 2 = 10 \] Next, add 2 to both sides to isolate the term with \( x \): \[ \frac{2}{3}x = 12 \] Then, multiply both sides by \( \frac{3}{2} \) to solve for \( x \): \[ x = 18 \] So, Melanie started with 18 vacuum cleaners. The final answer is \(\boxed{18}\).