FATIMA IS 12 years younger than Aslam . 6years later ASLAM will be twice as old as fatima .find their present ages

{ "query": { "display": "FATIMA IS 12 years younger than Aslam . 6years later ASLAM will be twice as old as fatima .find their present ages", "symbolab_question": "#FATIMA IS 12 years younger than Aslam . 6years later ASLAM will be twice as old as fatima .find their present ages" }, "solution": { "level": "PERFORMED", "subject": "Word Problems GPT", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Fatima}'s\\:age\\:is:}\\:6<br/>\\mathrm{\\mathrm{Aslam}'s\\:age\\:is:}\\:18" }, "steps": { "type": "interim", "title": "FATIMA IS 12 years younger than Aslam.<br/>6 years later ASLAM will be twice as old as fatima.<br/>find their present ages<br/> <br/>\\mathrm{Fatima}'s age is: $$6$$<br/>\\mathrm{Aslam}'s age is: $$18$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}x+12+6=2\\left(x+6\\right)$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Fatima}\\::\\:x<br/>\\mathrm{Aslam}\\::\\:x+12" }, { "type": "step", "primary": "Ages in 6 years", "result": "\\mathrm{Fatima}\\::\\:x+6<br/>\\mathrm{Aslam}\\::\\:x+12+6" }, { "type": "step", "primary": "Write an equation for their ages in 6 years", "result": "x+12+6=2\\left(x+6\\right)" } ] }, { "type": "interim", "title": "Solve for $$x,\\:x+12+6=2\\left(x+6\\right):{\\quad}x=6$$", "input": "x+12+6=2\\left(x+6\\right)", "steps": [ { "type": "step", "primary": "Add the numbers: $$12+6=18$$", "result": "x+18=2\\left(x+6\\right)" }, { "type": "interim", "title": "Expand $$2\\left(x+6\\right):{\\quad}2x+12$$", "input": "2\\left(x+6\\right)", "steps": [ { "type": "step", "primary": "Apply the distributive law: $$a\\left(b+c\\right)=ab+ac$$", "secondary": [ "$$a=2,\\:b=x,\\:c=6$$" ], "result": "=2x+2\\cdot\\:6", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:6=12$$", "result": "=2x+12" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7TzHQc0GUy2zFUJDz1aUISQsBmUOGgB0VAXoAXik9qC9EoApuujwRq/Ms3wa4gNT89ZVSO0B13oSpK+zJfqv7kB7MWKURN+43KCOzRc+RXaHgCE9D3PKbziCyAsniKTYl" } }, { "type": "step", "result": "x+18=2x+12" }, { "type": "interim", "title": "Move $$18\\:$$to the right side", "input": "x+18=2x+12", "result": "x=2x-6", "steps": [ { "type": "step", "primary": "Subtract $$18$$ from both sides", "result": "x+18-18=2x+12-18" }, { "type": "step", "primary": "Simplify", "result": "x=2x-6" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Move $$2x\\:$$to the left side", "input": "x=2x-6", "result": "-x=-6", "steps": [ { "type": "step", "primary": "Subtract $$2x$$ from both sides", "result": "x-2x=2x-6-2x" }, { "type": "step", "primary": "Simplify", "result": "-x=-6" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-1$$", "input": "-x=-6", "result": "x=6", "steps": [ { "type": "step", "primary": "Divide both sides by $$-1$$", "result": "\\frac{-x}{-1}=\\frac{-6}{-1}" }, { "type": "step", "primary": "Simplify", "result": "x=6" } ], "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{Fatima}\\::\\:6<br/>\\mathrm{Aslam}\\::\\:6+12" }, { "type": "step", "result": "6+12=18" } ] }, { "type": "step", "result": "\\mathrm{\\mathrm{Fatima}'s\\:age\\:is:}\\:6<br/>\\mathrm{\\mathrm{Aslam}'s\\:age\\:is:}\\:18" } ] } }