Michael is 12 years older than Brandon. Seventeen years ago, Michael was 4 times as old as Brandon.

{ "query": { "display": "Michael is 12 years older than Brandon. Seventeen years ago, Michael was 4 times as old as Brandon.", "symbolab_question": "#Michael is 12 years older than Brandon. Seventeen years ago, Michael was 4 times as old as Brandon." }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Michael}'s\\:age\\:is:}\\:33<br/>\\mathrm{\\mathrm{Brandon}'s\\:age\\:is:}\\:21" }, "steps": { "type": "interim", "title": "Michael is 12 years older than Brandon.<br/>17 years ago Michael was 4 times as old as Brandon<br/> <br/>\\mathrm{Michael}'s age is: $$33$$<br/>\\mathrm{Brandon}'s age is: $$21$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}x-17=4\\left(x-12-17\\right)$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Michael}\\::\\:x<br/>\\mathrm{Brandon}\\::\\:x-12" }, { "type": "step", "primary": "Ages 17 years ago", "result": "\\mathrm{Michael}\\::\\:x-17<br/>\\mathrm{Brandon}\\::\\:x-12-17" }, { "type": "step", "primary": "Write an equation for their ages 17 years ago", "result": "x-17=4\\left(x-12-17\\right)" } ] }, { "type": "interim", "title": "Solve for $$x,\\:x-17=4\\left(x-12-17\\right):{\\quad}x=33$$", "input": "x-17=4\\left(x-12-17\\right)", "steps": [ { "type": "interim", "title": "Expand $$4\\left(x-12-17\\right):{\\quad}4x-116$$", "input": "4\\left(x-12-17\\right)", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$-12-17=-29$$", "result": "=4\\left(x-29\\right)" }, { "type": "step", "primary": "Apply the distributive law: $$a\\left(b-c\\right)=ab-ac$$", "secondary": [ "$$a=4,\\:b=x,\\:c=29$$" ], "result": "=4x-4\\cdot\\:29", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "step", "primary": "Multiply the numbers: $$4\\cdot\\:29=116$$", "result": "=4x-116" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7WwVXNikyUuZVfZ3rwMwCugm6l6URy9L8j3HnsNdSBDp1DFKHA6Ddb5RE0Ay7mw9rpVjCuiAuXb1FPodh3Y0nfXql8XXPq6bNQlMm+36iNhl0OJNWmzc19TfDNjJ7Ur7LWKMi5N9gIeQFx8lSsWJSqw==" } }, { "type": "step", "result": "x-17=4x-116" }, { "type": "interim", "title": "Move $$17\\:$$to the right side", "input": "x-17=4x-116", "result": "x=4x-99", "steps": [ { "type": "step", "primary": "Add $$17$$ to both sides", "result": "x-17+17=4x-116+17" }, { "type": "step", "primary": "Simplify", "result": "x=4x-99" } ], "meta": { "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7JRKQUsimuPCn0/qoQN1HCXfDEHHItYfx4pT4tFrV9J/rAq6avuDivkRx4cMxEKqC/s6UagsV/VfiGuBypkfLziJ3jqIXHufAJ26xMxEh0JoUvCiCMv6AqmeZYB7NCCWQU9ik5WINGrsWotLzS7/BjMilG2DUqMrP9Xo55x7KtrDbW1CT6iTiD10pfBbS+/CQdXAkKm6UI3vQXWLxSyQBGjE7R2txk+hScQa/FoYzqcxKAe6yrVUi82Gw57Txpyk8YSL2zjjONXhPtUoRVt++JEDo8gwiZuu/FGE9+XfF1v39O9KhIT/uGg9DQjuXa49Ep+llO8m1JUsHsxYSyr5CjVb7qlKGJCpgSun0kdnDZYJH6n09x0sZXZjbeq1HH78kgsqwDvczEA2coxIljO6iORzS2phEsol5BFTVOAXt8l5V96z+yd/NTgi3X+wu1lkQ72wZm7kDUxdE6YSmfEbr2ji36mWG1fuZwrrwB0C3LJqcqeFNvkW4u+eykK6QpWbUbqgCeJqTEq1trtv68VFB6w==" } }, { "type": "interim", "title": "Move $$4x\\:$$to the left side", "input": "x=4x-99", "result": "-3x=-99", "steps": [ { "type": "step", "primary": "Subtract $$4x$$ from both sides", "result": "x-4x=4x-99-4x" }, { "type": "step", "primary": "Simplify", "result": "-3x=-99" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-3$$", "input": "-3x=-99", "result": "x=33", "steps": [ { "type": "step", "primary": "Divide both sides by $$-3$$", "result": "\\frac{-3x}{-3}=\\frac{-99}{-3}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{-3x}{-3}=\\frac{-99}{-3}", "result": "x=33", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{-3x}{-3}:{\\quad}x$$", "input": "\\frac{-3x}{-3}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{3x}{3}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{3}{3}=1$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7d0tdjDxEyTnOrs1nrB6oR3yRHuGw7+tM5METTDj6vVEed1oZgJr3Rrt+25B4RF18ZEt3ZXAiqUE0HIXrrrezJHZKl2mV4AlztiApTAFigz3d0VXHGredXQtr3h63wFDVialcV/dI5TH4fXyp+ncwuA==" } }, { "type": "interim", "title": "Simplify $$\\frac{-99}{-3}:{\\quad}33$$", "input": "\\frac{-99}{-3}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{99}{3}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{99}{3}=33$$", "result": "=33" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7dtzc2tFlsqyMXaOV7DX0WXyRHuGw7+tM5METTDj6vVFB9ghAhkH4WIU/Uuy0VhuUP8vQyhiD4JSfqjIvcQ7timkSOxgqdB0M/sw8Nt2sXXQ5jQF1Ks+hGKGTiOWcMIZSV2XjVNEekh8JtG3ZXDlTQQ==" } }, { "type": "step", "result": "x=33" } ] } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "interim", "title": "Find age", "steps": [ { "type": "step", "primary": "Plug in the value for $$x\\:$$to find current ages:", "result": "\\mathrm{Michael}\\::\\:33<br/>\\mathrm{Brandon}\\::\\:33-12" }, { "type": "step", "result": "33-12=21" } ] }, { "type": "step", "result": "\\mathrm{\\mathrm{Michael}'s\\:age\\:is:}\\:33<br/>\\mathrm{\\mathrm{Brandon}'s\\:age\\:is:}\\:21" } ] } }