results: 31

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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
31 grpo-gsm8k-train-13ep-success_global_step_50 gsm8k_main(0) 30 Question: Darrell and Allen's ages are in the ratio of 7:11. If their total age now is 162, calculate Allen's age 10 years from now. 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: Darrell and Allen's ages are in the ratio of 7:11. If their total age now is 162, calculate Allen's age 10 years from now. Answer:<|im_end|> <|im_start|>assistant 109 1 [109] [stop:-] To solve this problem, we need to determine the current ages of Darrell and Allen, and then calculate their ages 10 years from now. 1. **Define the variables:** Let \( D \) be Darrell's current age and \( A \) be Allen's current age. According to the problem, the ratio of their ages is 7:11. Therefore, we can write: \[ \frac{D}{A} = \frac{7}{11} \] 2. **Set up the equation:** We also know that the sum of their ages is 162: \[ D + A = 162 \] 3. **Express one variable in terms of the other:** From the ratio, we can express \( D \) in terms of \( A \): \[ D = \frac{7}{11}A \] 4. **Substitute into the sum equation:** Substitute \( D = \frac{7}{11}A \) into \( D + A = 162 \): \[ \frac{7}{11}A + A = 162 \] 5. **Combine like terms:** To combine the terms on the left side, we need a common denominator: \[ \frac{7A + 11A}{11} = 162 \] \[ \frac{18A}{11} = 162 \] 6. **Solve for \( A \):** Multiply both sides by 11 to clear the fraction: \[ 18A = 162 \times 11 \] \[ 18A = 1782 \] Divide both sides by 18: \[ A = \frac{1782}{18} \] \[ A = 99 \] 7. **Find Darrell's current age:** Using \( D = \frac{7}{11}A \): \[ D = \frac{7}{11} \times 99 \] \[ D = 63 \] 8. **Calculate Allen's age 10 years from now:** \[ A_{\text{10 years later}} = A + 10 \] \[ A_{\text{10 years later}} = 99 + 10 \] \[ A_{\text{10 years later}} = 109 \] Therefore, Allen's age 10 years from now is \(\boxed{109}\).