a mother is 3 times as old as her daughter. The sum of their ages is 60. How old is the mother.

{ "query": { "display": "a mother is 3 times as old as her daughter. The sum of their ages is 60. How old is the mother.", "symbolab_question": "#a mother is 3 times as old as her daughter. The sum of their ages is 60. How old is the mother." }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Mother}'s\\:age\\:is:}\\:45" }, "steps": { "type": "interim", "title": "a mother is 3 times as old as her daughter.<br/>The sum of their ages is 60.<br/>How old is the mother<br/> <br/>\\mathrm{Mother}'s age is: $$45$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}3x+x=60$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Daughter}\\::\\:x<br/>\\mathrm{Mother}\\::\\:3x" }, { "type": "step", "primary": "Write an equation for their ages ", "result": "3x+x=60" } ] }, { "type": "interim", "title": "Solve for $$x,\\:3x+x=60:{\\quad}x=15$$", "input": "3x+x=60", "steps": [ { "type": "step", "primary": "Add similar elements: $$3x+x=4x$$", "result": "4x=60" }, { "type": "interim", "title": "Divide both sides by $$4$$", "input": "4x=60", "result": "x=15", "steps": [ { "type": "step", "primary": "Divide both sides by $$4$$", "result": "\\frac{4x}{4}=\\frac{60}{4}" }, { "type": "step", "primary": "Simplify", "result": "x=15" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "interim", "title": "Find Mother's age$$:{\\quad}45$$", "steps": [ { "type": "step", "primary": "Plug in the value for $$x\\:$$to find current ages:", "result": "\\mathrm{Daughter}\\::\\:15<br/>\\mathrm{Mother}\\::\\:3\\cdot\\:15" }, { "type": "step", "result": "3\\cdot\\:15=45" } ] }, { "type": "step", "result": "\\mathrm{\\mathrm{Mother}'s\\:age\\:is:}\\:45" } ] } }