Alex is three times older than his brother now. In two years, he will be two times older than his brother. How old is his brother now?

{ "query": { "display": "Alex is three times older than his brother now. In two years, he will be two times older than his brother. How old is his brother now?", "symbolab_question": "#Alex is three times older than his brother now. In two years, he will be two times older than his brother. How old is his brother now?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Brother}'s\\:age\\:is:}\\:2" }, "steps": { "type": "interim", "title": "Alex is 3 times older than his brother now.<br/>In 2 years he will be 2 times older than his brother.<br/>How old is his brother now?<br/> <br/>\\mathrm{Brother}'s age is: $$2$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}3x+2=2\\left(x+2\\right)$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Brother}\\::\\:x<br/>\\mathrm{Alex}\\::\\:3x" }, { "type": "step", "primary": "Ages in 2 years", "result": "\\mathrm{Brother}\\::\\:x+2<br/>\\mathrm{Alex}\\::\\:3x+2" }, { "type": "step", "primary": "Write an equation for their ages in 2 years", "result": "3x+2=2\\left(x+2\\right)" } ] }, { "type": "interim", "title": "Solve for $$x,\\:3x+2=2\\left(x+2\\right):{\\quad}x=2$$", "input": "3x+2=2\\left(x+2\\right)", "steps": [ { "type": "interim", "title": "Expand $$2\\left(x+2\\right):{\\quad}2x+4$$", "input": "2\\left(x+2\\right)", "steps": [ { "type": "step", "primary": "Apply the distributive law: $$a\\left(b+c\\right)=ab+ac$$", "secondary": [ "$$a=2,\\:b=x,\\:c=2$$" ], "result": "=2x+2\\cdot\\:2", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2=4$$", "result": "=2x+4" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7GNfWctW+X0YgsLFbTt58uAsBmUOGgB0VAXoAXik9qC9EoApuujwRq/Ms3wa4gNT89ZVSO0B13oSpK+zJfqv7kB7MWKURN+43KCOzRc+RXaHGhfvabr7FAlf4+ei9Aanz" } }, { "type": "step", "result": "3x+2=2x+4" }, { "type": "interim", "title": "Move $$2\\:$$to the right side", "input": "3x+2=2x+4", "result": "3x=2x+2", "steps": [ { "type": "step", "primary": "Subtract $$2$$ from both sides", "result": "3x+2-2=2x+4-2" }, { "type": "step", "primary": "Simplify", "result": "3x=2x+2" } ], "meta": { "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7flVHZXrJIimVj2dyJ1AawxXdh5TFm8xOUqmxPJpykP3IR7tX/W1jaTzwT4+VN53qS8DfmRBUqpCWOuo05WrN0LWhruMAPwTV7+YBH7BG1EZl2mXSrAJmEjAI3GZ2D0DB0hYzF6vxjSZoMSInCY/PPQbO95/2yiZOrh8Vdx/OHPtL0rMteoF5FEvu8HePHkHFwR7ozpvYejNDhMzAkmmyPzYjWduedB5bCyGSfyAHqqS9a8WlVLwuKidt1hhLyyF8sh2QamHomSJbPCVBX9Ttpn9wduzV3qTprD8aTlgjwHJclIZfLzRJ3bRksUs1lMp48hXn+PJfFc3Uh1JOPr5wj0iZ3bB0BgUtwTNr3KnZpFWw14FmAV06QSwgd736/nVs5nTxhhX/JMpykzZI6J3VrKGoxMw626x3PqNkZlKxJbSBBTEk/JQ2cZ9WKuRzClU7yPZ7i1yLlu72snBS8fQgEbEdNOgCNOpEVDz+m2v+YkGfqH9JwAAHWwoAaZnvIAzm" } }, { "type": "interim", "title": "Move $$2x\\:$$to the left side", "input": "3x=2x+2", "result": "x=2", "steps": [ { "type": "step", "primary": "Subtract $$2x$$ from both sides", "result": "3x-2x=2x+2-2x" }, { "type": "step", "primary": "Simplify", "result": "x=2" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "step", "result": "\\mathrm{\\mathrm{Brother}'s\\:age\\:is:}\\:2" } ] } }