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-test-30ep-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, so we can write: \[ \frac{D}{A} = \frac{7}{11} \] This implies: \[ D = \frac{7}{11}A \] 2. **Set up the equation for their total age:** The sum of their current ages is 162: \[ D + A = 162 \] Substitute \( D = \frac{7}{11}A \) into the equation: \[ \frac{7}{11}A + A = 162 \] Combine the terms on the left side: \[ \frac{7A + 11A}{11} = 162 \] Simplify the numerator: \[ \frac{18A}{11} = 162 \] Solve for \( A \): \[ 18A = 162 \times 11 \] \[ 18A = 1782 \] \[ A = \frac{1782}{18} \] \[ A = 99 \] 3. **Calculate Darrell's current age:** Using \( D = \frac{7}{11}A \): \[ D = \frac{7}{11} \times 99 \] \[ D = 7 \times 9 \] \[ D = 63 \] 4. **Calculate Allen's age 10 years from now:** Allen's current age is 99, so 10 years from now: \[ A_{\text{future}} = 99 + 10 = 109 \] Thus, Allen's age 10 years from now is \(\boxed{109}\). |