Tim's age is half of Joe's age. Emma is four years older than Joe. The sum of Tim, Emma, and Joe's age is 54. How old is Joe?

{ "query": { "display": "Tim's age is half of Joe's age. Emma is four years older than Joe. The sum of Tim, Emma, and Joe's age is 54. How old is Joe?", "symbolab_question": "#Tim's age is half of Joe's age. Emma is four years older than Joe. The sum of Tim, Emma, and Joe's age is 54. How old is Joe?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Joe}'s\\:age\\:is:}\\:20" }, "steps": { "type": "interim", "title": "Tim's age is 1/2 of Joe's age.<br/>Emma is 4 years older than Joe.<br/>The sum of Tim Emma and Joe's age is 54.<br/>How old is Joe?<br/> <br/>\\mathrm{Joe}'s age is: $$20$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}\\frac{1}{2}x+x+4+x=54$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Joe}\\::\\:x<br/>\\mathrm{Emma}\\::\\:x+4<br/>\\mathrm{Tim}\\::\\:\\frac{1}{2}x" }, { "type": "step", "primary": "Write an equation for their ages ", "result": "\\frac{1}{2}x+x+4+x=54" } ] }, { "type": "interim", "title": "Solve for $$x,\\:\\frac{1}{2}x+x+4+x=54:{\\quad}x=20$$", "input": "\\frac{1}{2}x+x+4+x=54", "steps": [ { "type": "step", "primary": "Group like terms", "result": "\\frac{1}{2}x+x+x+4=54" }, { "type": "step", "primary": "Add similar elements: $$x+x=2x$$", "result": "\\frac{1}{2}x+2x+4=54" }, { "type": "interim", "title": "Move $$4\\:$$to the right side", "input": "\\frac{1}{2}x+2x+4=54", "result": "\\frac{1}{2}x+2x=50", "steps": [ { "type": "step", "primary": "Subtract $$4$$ from both sides", "result": "\\frac{1}{2}x+2x+4-4=54-4" }, { "type": "step", "primary": "Simplify", "result": "\\frac{1}{2}x+2x=50" } ], "meta": { "gptData": 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"5x=100", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{1}{2}x\\cdot\\:2:{\\quad}x$$", "input": "\\frac{1}{2}x\\cdot\\:2", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{1\\cdot\\:2}{2}x" }, { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=x\\cdot\\:1" }, { "type": "step", "primary": "Multiply: $$x\\cdot\\:1=x$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7TayuIlGCNKzKncs66z+Jzv4CsFtYCGVpnwQ6GR+/iwQJQJZuTAY5js+oqjdT8ksls9TeFoc2NYtMR3HLuoQQfosaY2cs9YZ/08feWmaOgkhY2wgLqGp4cI6P/WzKf+9pwhztzjvVYzj7cLQmsrJ9hg==" } }, { "type": "interim", "title": "Simplify $$2x\\cdot\\:2:{\\quad}4x$$", "input": "2x\\cdot\\:2", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2=4$$", "result": "=4x" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7bb+glc6253U2NNlq0+VfJCAn9lkDfZkicUGkO3EF+IqEnXlKdJOvXJDOfm408RPrgQUxJPyUNnGfVirkcwpVO3RNt9xNvrn0uR65TGUcKLqyGKuJM4vlS6f3PxoaigvX" } }, { "type": "interim", "title": "Simplify $$50\\cdot\\:2:{\\quad}100$$", "input": "50\\cdot\\:2", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$50\\cdot\\:2=100$$", "result": "=100" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79NpwsSxjkgTBUKs1iKFfNyAn9lkDfZkicUGkO3EF+IpEQE1fSSv3FpKZh7xb9viX72wZm7kDUxdE6YSmfEbr2vbYkG7WYo50Y10Zhp7treHxXvVsFxz/j+YxsmEvnlJ6" } }, { "type": "step", "result": "x+4x=100" }, { "type": "step", "result": "5x=100" } ] } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$5$$", "input": "5x=100", "result": "x=20", "steps": [ { "type": "step", "primary": "Divide both sides by $$5$$", "result": "\\frac{5x}{5}=\\frac{100}{5}" }, { "type": "step", "primary": "Simplify", "result": "x=20" } ], "meta": { "gptData": 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