jack is twice as old as jill. Ten years from now, the sum of their ages will be 50. Find the present age of each

{ "query": { "display": "jack is twice as old as jill. Ten years from now, the sum of their ages will be 50. Find the present age of each", "symbolab_question": "#jack is twice as old as jill. Ten years from now, the sum of their ages will be 50. Find the present age of each" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Jill}'s\\:age\\:is:}\\:10<br/>\\mathrm{\\mathrm{Jack}'s\\:age\\:is:}\\:20" }, "steps": { "type": "interim", "title": "jack is twice as old as jill.<br/>10 years from now the sum of their ages will be 50.<br/>Find the present age of each<br/> <br/>\\mathrm{Jill}'s age is: $$10$$<br/>\\mathrm{Jack}'s age is: $$20$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}2x+10+x+10=50$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Jill}\\::\\:x<br/>\\mathrm{Jack}\\::\\:2x" }, { "type": "step", "primary": "Ages in 10 years", "result": "\\mathrm{Jill}\\::\\:x+10<br/>\\mathrm{Jack}\\::\\:2x+10" }, { "type": "step", "primary": "Write an equation for their ages in 10 years", "result": "2x+10+x+10=50" } ] }, { "type": "interim", "title": "Solve for $$x,\\:2x+10+x+10=50:{\\quad}x=10$$", "input": "2x+10+x+10=50", "steps": [ { "type": "step", "primary": "Group like terms", "result": "2x+x+10+10=50" }, { "type": "step", "primary": "Add similar elements: $$2x+x=3x$$", "result": "3x+10+10=50" }, { "type": "step", "primary": "Add the numbers: $$10+10=20$$", "result": "3x+20=50" }, { "type": "interim", "title": "Move $$20\\:$$to the right side", "input": "3x+20=50", "result": "3x=30", "steps": [ { "type": "step", "primary": "Subtract $$20$$ from both sides", "result": "3x+20-20=50-20" }, { "type": "step", "primary": "Simplify", "result": "3x=30" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$3$$", "input": "3x=30", "result": "x=10", "steps": [ { "type": "step", "primary": "Divide both sides by $$3$$", "result": "\\frac{3x}{3}=\\frac{30}{3}" }, { "type": "step", "primary": "Simplify", "result": "x=10" } ], "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{Jill}\\::\\:10<br/>\\mathrm{Jack}\\::\\:2\\cdot\\:10" }, { "type": "step", "result": "2\\cdot\\:10=20" } ] }, { "type": "step", "result": "\\mathrm{\\mathrm{Jill}'s\\:age\\:is:}\\:10<br/>\\mathrm{\\mathrm{Jack}'s\\:age\\:is:}\\:20" } ] } }