John is 5 years older than ellen, and 3 years ago the sum of their ages was 17. how old is John?

{ "query": { "display": "John is 5 years older than ellen, and 3 years ago the sum of their ages was 17. how old is John?", "symbolab_question": "#John is 5 years older than ellen, and 3 years ago the sum of their ages was 17. how old is John?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{John}'s\\:age\\:is:}\\:14" }, "steps": { "type": "interim", "title": "John is 5 years older than ellen.<br/>3 years ago the sum of their ages was 17.<br/>how old is John?<br/> <br/>\\mathrm{John}'s age is: $$14$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}x-3+x-5-3=17$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{John}\\::\\:x<br/>\\mathrm{Ellen}\\::\\:x-5" }, { "type": "step", "primary": "Ages 3 years ago", "result": "\\mathrm{John}\\::\\:x-3<br/>\\mathrm{Ellen}\\::\\:x-5-3" }, { "type": "step", "primary": "Write an equation for their ages 3 years ago", "result": "x-3+x-5-3=17" } ] }, { "type": "interim", "title": "Solve for $$x,\\:x-3+x-5-3=17:{\\quad}x=14$$", "input": "x-3+x-5-3=17", "steps": [ { "type": "step", "primary": "Group like terms", "result": "x+x-3-5-3=17" }, { "type": "step", "primary": "Add similar elements: $$x+x=2x$$", "result": "2x-3-5-3=17" }, { "type": "step", "primary": "Subtract the numbers: $$-3-5-3=-11$$", "result": "2x-11=17" }, { "type": "interim", "title": "Move $$11\\:$$to the right side", "input": "2x-11=17", "result": "2x=28", "steps": [ { "type": "step", "primary": "Add $$11$$ to both sides", "result": "2x-11+11=17+11" }, { "type": "step", "primary": "Simplify", "result": "2x=28" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$2$$", "input": "2x=28", "result": "x=14", "steps": [ { "type": "step", "primary": "Divide both sides by $$2$$", "result": "\\frac{2x}{2}=\\frac{28}{2}" }, { "type": "step", "primary": "Simplify", "result": "x=14" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "step", "result": "\\mathrm{\\mathrm{John}'s\\:age\\:is:}\\:14" } ] } }