{ "query": { "display": "Emma is 10 years old. Her mother is 30 years older than Emma. How old is her mother", "symbolab_question": "#Emma is 10 years old. Her mother is 30 years older than Emma. How old is her mother" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Mother}'s\\:age\\:is:}\\:40" }, "steps": { "type": "interim", "title": "Emma is 10 years old.<br/>Her mother is 30 years older than Emma.<br/>How old is her mother<br/> <br/>\\mathrm{Mother}'s age is: $$40$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}x-30=10$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Mother}\\::\\:x<br/>\\mathrm{Emma}\\::\\:10" }, { "type": "step", "primary": "Write an equation for their ages ", "result": "x-30=10" } ] }, { "type": "interim", "title": "Solve for $$x,\\:x-30=10:{\\quad}x=40$$", "input": "x-30=10", "steps": [ { "type": "interim", "title": "Move $$30\\:$$to the right side", "input": "x-30=10", "result": "x=40", "steps": [ { "type": "step", "primary": "Add $$30$$ to both sides", "result": "x-30+30=10+30" }, { "type": "step", "primary": "Simplify", "result": "x=40" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "step", "result": "\\mathrm{\\mathrm{Mother}'s\\:age\\:is:}\\:40" } ] } }