Nicole is half as old as Donald. The sum of their ages is 72.How old is Nicole, in years?

{ "query": { "display": "Nicole is half as old as Donald. The sum of their ages is 72.How old is Nicole, in years?", "symbolab_question": "#Nicole is half as old as Donald. The sum of their ages is 72.How old is Nicole, in years?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Nicole}'s\\:age\\:is:}\\:24" }, "steps": { "type": "interim", "title": "Nicole is 1/2 as old as Donald.<br/>The sum of their ages is 72.<br/>How old is Nicole in years?<br/> <br/>\\mathrm{Nicole}'s age is: $$24$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}\\frac{1}{2}x+x=72$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Donald}\\::\\:x<br/>\\mathrm{Nicole}\\::\\:\\frac{1}{2}x" }, { "type": "step", "primary": "Write an equation for their ages ", "result": "\\frac{1}{2}x+x=72" } ] }, { "type": "interim", "title": "Solve for $$x,\\:\\frac{1}{2}x+x=72:{\\quad}x=48$$", "input": "\\frac{1}{2}x+x=72", "steps": [ { "type": "interim", "title": "Multiply both sides by $$2$$", "input": "\\frac{1}{2}x+x=72", "result": "3x=144", "steps": [ { "type": "step", "primary": "Multiply both sides by $$2$$", "result": "\\frac{1}{2}x\\cdot\\:2+x\\cdot\\:2=72\\cdot\\:2" }, { "type": "interim", "title": "Simplify", "input": "\\frac{1}{2}x\\cdot\\:2+x\\cdot\\:2=72\\cdot\\:2", "result": "3x=144", "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 $$x\\cdot\\:2:{\\quad}2x$$", "input": "x\\cdot\\:2", "steps": [ { "type": "step", "primary": "Apply the commutative law: $$x\\cdot\\:2=2x$$", "result": "2x" } ], "meta": { "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7HssHMI75B51lE/BFEeezwN13jtrSFDx+UNsawjlOjV0jasC1sq5rW82u/JAvG/1i1sD7NfhsPe7eDHrmjY0mE4QsyQIO3WXmmXx+O0KtEOMhfm92Y7qNlJFIbiF0TOFB" } }, { "type": "interim", "title": "Simplify $$72\\cdot\\:2:{\\quad}144$$", "input": "72\\cdot\\:2", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$72\\cdot\\:2=144$$", "result": "=144" } ], "meta": { "solvingClass": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7gHBw7VpoKmLYPoHxrr8uqCAn9lkDfZkicUGkO3EF+IosnJH21THw8hchBT6XNs5P72wZm7kDUxdE6YSmfEbr2rjwYWrTTdgwnKiNNe98H1RDwj8AmrMHPWBzoj9AZ3CG" } }, { "type": "step", "result": "x+2x=144" }, { "type": "step", "result": "3x=144" } ] } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$3$$", "input": "3x=144", "result": "x=48", "steps": [ { "type": "step", "primary": "Divide both sides by $$3$$", "result": "\\frac{3x}{3}=\\frac{144}{3}" }, { "type": "step", "primary": "Simplify", "result": "x=48" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "interim", "title": "Find Nicole's age$$:{\\quad}24$$", "steps": [ { "type": "step", "primary": "Plug in the value for $$x\\:$$to find current ages:", "result": "\\mathrm{Donald}\\::\\:48<br/>\\mathrm{Nicole}\\::\\:\\frac{1}{2}\\cdot\\:48" }, { "type": "step", "result": "\\frac{1}{2}\\cdot\\:48=24" } ] }, { "type": "step", "result": "\\mathrm{\\mathrm{Nicole}'s\\:age\\:is:}\\:24" } ] } }