[{"id":"747d7626-32a6-4f98-8555-7d4eeeea3062","created_at":"2025-03-17T17:44:47Z","branch_list":["00000000-0000-4000-0000-000000000000","19c1fed0-8a2e-4df9-b4ab-5fe532fdca7c","524f883c-0ce7-46e0-9cd2-b6f994b46006"],"state":"done","prompt":"I stole a ball and a bat that together cost $1.10. The bat is $1 more than the ball. What did I pay for the ball?","reply":"<p>Let's denote the cost of the ball as <span><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>x</mi></mrow></math></span> dollars. According to the problem:</p>\n<ul>\n<li>The bat costs $1 more than the ball, so the cost of the bat is <span><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></math></span> dollars.</li>\n<li>Together, the ball and bat cost $1.10.</li>\n</ul>\n<p>We can set up the equation based on this information:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mi>x</mi><mo>+</mo><mo stretchy=\"false\">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy=\"false\">)</mo><mo>=</mo><mn>1.10</mn></mrow></math></div>\n</p>\n<p>Simplifying this equation:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>1.10</mn></mrow></math></div>\n</p>\n<p>Subtracting 1 from both sides:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mn>2</mn><mi>x</mi><mo>=</mo><mn>0.10</mn></mrow></math></div>\n</p>\n<p>Dividing both sides by 2:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mi>x</mi><mo>=</mo><mn>0.05</mn></mrow></math></div>\n</p>\n<p>Thus, the cost of the ball is <strong>$0.05</strong> (5 cents). </p>\n<p>Therefore, you paid <strong>$0.05</strong> for the ball.</p>","md":"Let's denote the cost of the ball as \\( x \\) dollars. According to the problem:\n\n- The bat costs $1 more than the ball, so the cost of the bat is \\( x + 1 \\) dollars.\n- Together, the ball and bat cost $1.10.\n\nWe can set up the equation based on this information:\n\n\\[\nx + (x + 1) = 1.10\n\\]\n\nSimplifying this equation:\n\n\\[\n2x + 1 = 1.10\n\\]\n\nSubtracting 1 from both sides:\n\n\\[\n2x = 0.10\n\\]\n\nDividing both sides by 2:\n\n\\[\nx = 0.05\n\\]\n\nThus, the cost of the ball is **$0.05** (5 cents). \n\nTherefore, you paid **$0.05** for the ball.","profile":{"id":null,"name":null,"model":"gpt-4o-mini","model_name":"GPT 4o mini","model_provider":"openai","model_input_limit":1000000,"recommended":false,"model_info":"\n\n<div class=\"heading\">\n <div class=\"left\">\n \n \n \n <svg class=\"model-icon icon-xs\" data-model=\"gpt-4o-mini\">\n <use href=\"#icon-openai\"/>\n </svg>\n <h3>\n \n <span class=\"model-provider\">OpenAI</span>\n \n <span class=\"model-name\">none</span>\n </h3>\n </div>\n\n \n <a href=\"/settings?p=custom_assistant&id=none\">\n <svg class=\"icon-sm edit-icon\" aria-hidden=\"true\">\n <use href=\"#icon-pencil\" />\n </svg>\n </a>\n \n</div>\n\n\n<hr />\n<ul>\n \n <li>\n <h4>\n Cost\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Relatively cheap\">\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n </div>\n</span>\n </li>\n <li>\n <h4>\n Quality\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Rated 2 out of 5\">\n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n </div>\n</span>\n </li>\n <li>\n <h4>\n Speed\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Rated 5 out of 5\">\n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n </div>\n</span>\n </li>\n <li class=\"divider\" aria-hidden=\"true\"></li>\n <li>\n <h4>Last updated</h4>\n <span class=\"date\">\n \n \n 2024-07-18\n \n \n </span>\n </li>\n \n</ul>","model_provider_name":"OpenAI","internet_access":false,"personalizations":true,"shortcut":null,"is_default_profile":false},"metadata":"<li>\n <span class=\"attribute\">Model</span>\n <span class=\"value\"><i class=\"icon-xs mr-2\"><svg><use href=\"#icon-openai\"></use></svg></i>GPT 4o mini</span>\n</li>\n<li>\n <span class=\"attribute\">Version</span>\n <span class=\"value\">gpt-4o-mini-2024-07-18</span>\n</li>\n<li>\n <span class=\"attribute\">Speed (tok/s)</span>\n <span class=\"value\">60</span>\n</li>\n<li>\n <span class=\"attribute\">Tokens</span>\n <span class=\"value\">1,254</span>\n</li>\n<li>\n <span class=\"attribute\">Cost ($)</span>\n <span class=\"value\">< 0.001</span>\n</li>\n<li>\n <span class=\"attribute\">End to end time (s)</span>\n <span class=\"value\">3.01</span>\n</li>\n","citations":[],"documents":[]},{"id":"0ff43cc0-73a6-4dc7-832a-c43b48c8fa13","created_at":"2025-03-17T17:45:21Z","state":"done","prompt":"Are you sure?","reply":"<p>Yes, I am sure. Let's go through the solution again step by step to confirm:</p>\n<ol>\n<li>Let the cost of the ball be <span><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>x</mi></mrow></math></span> dollars.</li>\n<li>The bat costs $1 more than the ball, so its cost is <span><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></math></span> dollars.</li>\n<li>The total cost of the ball and bat together is $1.10.</li>\n</ol>\n<p>We can set up the equation:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mi>x</mi><mo>+</mo><mo stretchy=\"false\">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy=\"false\">)</mo><mo>=</mo><mn>1.10</mn></mrow></math></div>\n</p>\n<p>This simplifies to:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>1.10</mn></mrow></math></div>\n</p>\n<p>Subtracting 1 from both sides gives:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mn>2</mn><mi>x</mi><mo>=</mo><mn>0.10</mn></mrow></math></div>\n</p>\n<p>Dividing both sides by 2 results in:</p>\n<p>\n<div class=\"math-box\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mrow><mi>x</mi><mo>=</mo><mn>0.05</mn></mrow></math></div>\n</p>\n<p>Thus, the cost of the ball is indeed <strong>$0.05</strong> (5 cents). The bat, being $1 more than the ball, would then cost <strong>$1.05</strong>. Together, they add up to <strong>$1.10</strong>. </p>\n<p>So, the answer is correct: you paid <strong>$0.05</strong> for the ball.</p>","md":"Yes, I am sure. Let's go through the solution again step by step to confirm:\n\n1. Let the cost of the ball be \\( x \\) dollars.\n2. The bat costs $1 more than the ball, so its cost is \\( x + 1 \\) dollars.\n3. The total cost of the ball and bat together is $1.10.\n\nWe can set up the equation:\n\n\\[\nx + (x + 1) = 1.10\n\\]\n\nThis simplifies to:\n\n\\[\n2x + 1 = 1.10\n\\]\n\nSubtracting 1 from both sides gives:\n\n\\[\n2x = 0.10\n\\]\n\nDividing both sides by 2 results in:\n\n\\[\nx = 0.05\n\\]\n\nThus, the cost of the ball is indeed **$0.05** (5 cents). The bat, being $1 more than the ball, would then cost **$1.05**. Together, they add up to **$1.10**. \n\nSo, the answer is correct: you paid **$0.05** for the ball.","profile":{"id":null,"name":null,"model":"gpt-4o-mini","model_name":"GPT 4o mini","model_provider":"openai","model_input_limit":1000000,"recommended":false,"model_info":"\n\n<div class=\"heading\">\n <div class=\"left\">\n \n \n \n <svg class=\"model-icon icon-xs\" data-model=\"gpt-4o-mini\">\n <use href=\"#icon-openai\"/>\n </svg>\n <h3>\n \n <span class=\"model-provider\">OpenAI</span>\n \n <span class=\"model-name\">none</span>\n </h3>\n </div>\n\n \n <a href=\"/settings?p=custom_assistant&id=none\">\n <svg class=\"icon-sm edit-icon\" aria-hidden=\"true\">\n <use href=\"#icon-pencil\" />\n </svg>\n </a>\n \n</div>\n\n\n<hr />\n<ul>\n \n <li>\n <h4>\n Cost\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Relatively cheap\">\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-cost --low\"></div>\n \n \n </div>\n</span>\n </li>\n <li>\n <h4>\n Quality\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Rated 2 out of 5\">\n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"unfilled-bubble\"></div>\n \n \n </div>\n</span>\n </li>\n <li>\n <h4>\n Speed\n </h4>\n <span>\n \n \n \n\n \n \n \n\n <div class=\"score\" aria-label=\"Rated 5 out of 5\">\n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n \n \n <div aria-hidden=\"true\" class=\"filled-bubble\"></div>\n \n \n </div>\n</span>\n </li>\n <li class=\"divider\" aria-hidden=\"true\"></li>\n <li>\n <h4>Last updated</h4>\n <span class=\"date\">\n \n \n 2024-07-18\n \n \n </span>\n </li>\n \n</ul>","model_provider_name":"OpenAI","internet_access":false,"personalizations":true,"shortcut":null,"is_default_profile":false},"metadata":"<li>\n <span class=\"attribute\">Model</span>\n <span class=\"value\"><i class=\"icon-xs mr-2\"><svg><use href=\"#icon-openai\"></use></svg></i>GPT 4o mini</span>\n</li>\n<li>\n <span class=\"attribute\">Version</span>\n <span class=\"value\">gpt-4o-mini-2024-07-18</span>\n</li>\n<li>\n <span class=\"attribute\">Speed (tok/s)</span>\n <span class=\"value\">97</span>\n</li>\n<li>\n <span class=\"attribute\">Tokens</span>\n <span class=\"value\">1,500</span>\n</li>\n<li>\n <span class=\"attribute\">Cost ($)</span>\n <span class=\"value\">< 0.001</span>\n</li>\n<li>\n <span class=\"attribute\">End to end time (s)</span>\n <span class=\"value\">2.42</span>\n</li>\n","citations":[],"documents":[]}]