{ "query": { "display": "A sofa is 12 years old and a table is 36 years old. In how many years will the table be twice as old as the sofa?", "symbolab_question": "#A sofa is 12 years old and a table is 36 years old. In how many years will the table be twice as old as the sofa?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{Number\\:of\\:\\mathrm{years\\:from\\:now}}:\\:12" }, "steps": { "type": "interim", "title": "A sofa is 12 years old.<br/>a table is 36 years old.<br/>In how many years will the table be twice as old as the sofa?<br/> <br/>Number of \\mathrm{years from now}$$:\\:12$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}2\\left(12+x\\right)=36+x$$", "steps": [ { "type": "step", "primary": "Represent in terms of $$x:$$", "result": "\\mathrm{Number\\:of\\:years}\\::\\:x<br/>\\mathrm{Sofa}\\::\\:12<br/>\\mathrm{Table}\\::\\:36" }, { "type": "step", "primary": "Ages $$x\\:$$years from now", "result": "\\mathrm{Sofa}\\::\\:12+x<br/>\\mathrm{Table}\\::\\:36+x" }, { "type": "step", "primary": "Write an equation for $$x\\:$$years from now", "result": "2\\left(12+x\\right)=36+x" } ] }, { "type": "interim", "title": "Solve for $$x,\\:2\\left(12+x\\right)=36+x:{\\quad}x=12$$", "input": "2\\left(12+x\\right)=36+x", "steps": [ { "type": "interim", "title": "Expand $$2\\left(12+x\\right):{\\quad}24+2x$$", "input": "2\\left(12+x\\right)", "steps": [ { "type": "step", "primary": "Apply the distributive law: $$a\\left(b+c\\right)=ab+ac$$", "secondary": [ "$$a=2,\\:b=12,\\:c=x$$" ], "result": "=2\\cdot\\:12+2x", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:12=24$$", "result": "=24+2x" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7gNDAJR9X54SyY8dXYNCrH3cUJadsLvGcDY7IUPYXjf6zs903yhxK0NInTwR7JvSRyM/29l7SHlwNleTQoRn0qBJyf8zawtgEaDEKWrMLEzZO5mLkZYFApJvvKCHfgbrm" } }, { "type": "step", "result": "24+2x=36+x" }, { "type": "interim", "title": "Move $$24\\:$$to the right side", "input": "24+2x=36+x", "result": "2x=x+12", "steps": [ { "type": "step", "primary": "Subtract $$24$$ from both sides", "result": "24+2x-24=36+x-24" }, { "type": "step", "primary": "Simplify", "result": "2x=x+12" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Move $$x\\:$$to the left side", "input": "2x=x+12", "result": "x=12", "steps": [ { "type": "step", "primary": "Subtract $$x$$ from both sides", "result": "2x-x=x+12-x" }, { "type": "step", "primary": "Simplify", "result": "x=12" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "step", "result": "\\mathrm{Number\\:of\\:\\mathrm{years\\:from\\:now}}:\\:12" } ] } }