Ricardo is 5 years older than April. In 6 years the sum of their ages will be 75. How old is Ricardo now?

{ "query": { "display": "Ricardo is 5 years older than April. In 6 years the sum of their ages will be 75. How old is Ricardo now?", "symbolab_question": "#Ricardo is 5 years older than April. In 6 years the sum of their ages will be 75. How old is Ricardo now?" }, "solution": { "level": "PERFORMED", "subject": "Word Problems", "topic": "Age", "subTopic": "Other", "default": "\\mathrm{\\mathrm{Ricardo}'s\\:age\\:is:}\\:34" }, "steps": { "type": "interim", "title": "Ricardo is 5 years older than April.<br/>In 6 years the sum of their ages will be 75.<br/>How old is Ricardo now?<br/> <br/>\\mathrm{Ricardo}'s age is: $$34$$", "steps": [ { "type": "interim", "title": "Translate the problem into an equation:$${\\quad}x+6+x-5+6=75$$", "steps": [ { "type": "step", "primary": "Represent ages in terms of $$x:$$", "result": "\\mathrm{Ricardo}\\::\\:x<br/>\\mathrm{April}\\::\\:x-5" }, { "type": "step", "primary": "Ages in 6 years", "result": "\\mathrm{Ricardo}\\::\\:x+6<br/>\\mathrm{April}\\::\\:x-5+6" }, { "type": "step", "primary": "Write an equation for their ages in 6 years", "result": "x+6+x-5+6=75" } ] }, { "type": "interim", "title": "Solve for $$x,\\:x+6+x-5+6=75:{\\quad}x=34$$", "input": "x+6+x-5+6=75", "steps": [ { "type": "step", "primary": "Group like terms", "result": "x+x+6-5+6=75" }, { "type": "step", "primary": "Add similar elements: $$x+x=2x$$", "result": "2x+6-5+6=75" }, { "type": "step", "primary": "Add/Subtract the numbers: $$6-5+6=7$$", "result": "2x+7=75" }, { "type": "interim", "title": "Move $$7\\:$$to the right side", "input": "2x+7=75", "result": "2x=68", "steps": [ { "type": "step", "primary": "Subtract $$7$$ from both sides", "result": "2x+7-7=75-7" }, { "type": "step", "primary": "Simplify", "result": "2x=68" } ], "meta": { "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$2$$", "input": "2x=68", "result": "x=34", "steps": [ { "type": "step", "primary": "Divide both sides by $$2$$", "result": "\\frac{2x}{2}=\\frac{68}{2}" }, { "type": "step", "primary": "Simplify", "result": "x=34" } ], "meta": { "gptData": "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" } } ], "meta": { "solvingClass": "Equations" } }, { "type": "step", "result": "\\mathrm{\\mathrm{Ricardo}'s\\:age\\:is:}\\:34" } ] } }