{"id":"cb_question_bank:a039e503-29ea-4704-ad3c-84c178e4b101","source_id":"cb_question_bank","source_item_id":"a039e503-29ea-4704-ad3c-84c178e4b101","external_id":"9074f61c-00b0-4492-ab66-501db8f46f38","ibn":null,"question_id":"9f6f96ff","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A wire with a length of 106 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 6 more than 4 times the value of y . What is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A wire with a length of <math alttext=\"106\"><mn>106</mn>\n</math> inches is cut into two parts. One part has a length of <math alttext=\"x\"><mi>x</mi>\n</math> inches, and the other part has a length of <math alttext=\"y\"><mi>y</mi>\n</math> inches. The value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math> more than <math alttext=\"4\"><mn>4</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. What is the value of <math alttext=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p>Choice D is correct. It's given that a wire with a length of <math alttext=\"106\"><mn>106</mn>\n</math> inches is cut into two parts. It's also given that one part has a length of <math alttext=\"x\"><mi>x</mi>\n</math> inches and the other part has a length of <math alttext=\"y\"><mi>y</mi>\n</math> inches. This can be represented by the equation <math alttext=\"x plus y equals 106\"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>106</mn></math>. It's also given that the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math> more than <math alttext=\"4\"><mn>4</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. This can be represented by the equation <math alttext=\"x equals 4 y plus 6\"><mi>x</mi><mo>=</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>6</mn></math>. Substituting <math alttext=\"4 y plus 6\"><mn>4</mn><mi>y</mi><mo>+</mo><mn>6</mn></math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation <math alttext=\"x plus y equals 106\"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>106</mn></math> yields <math alttext=\"4 y plus 6 plus y equals 106\"><mn>4</mn><mi>y</mi><mo>+</mo><mn>6</mn><mo>+</mo><mi>y</mi><mo>=</mo><mn>106</mn></math>, or <math alttext=\"5 y plus 6 equals 106\"><mn>5</mn><mi>y</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>106</mn></math>. Subtracting <math alttext=\"6\"><mn>6</mn>\n</math> from each side of this equation yields&nbsp;<math alttext=\"5 y equals 100\"><mn>5</mn><mi>y</mi><mo>=</mo><mn>100</mn></math>. Dividing each side of this equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields <math alttext=\"y equals 20\"><mi>y</mi><mo>=</mo><mn>20</mn></math>. Substituting <math alttext=\"20\"><mn>20</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the equation <math alttext=\"x equals 4 y plus 6\"><mi>x</mi><mo>=</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>6</mn></math> yields <math alttext=\"x equals 4 left parenthesis 20 right parenthesis plus 6\"><mi>x</mi><mo>=</mo><mn>4</mn><mo>(</mo><mn>20</mn><mo>)</mo><mo>+</mo><mn>6</mn></math>, or <math alttext=\"x equals 86\"><mi>x</mi><mo>=</mo><mn>86</mn></math>.&nbsp;</p>\n<p>Choice A is incorrect. This value represents less than half of the total length of <math alttext=\"106\"><mn>106</mn>\n</math> inches; however, <math alttext=\"x\"><mi>x</mi>\n</math> represents the length of the longer part of the wire, since it's given that the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math> more than <math alttext=\"4\"><mn>4</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>.</p>\n<p>Choice B is incorrect. This value represents less than half of the total length of <math alttext=\"106\"><mn>106</mn>\n</math> inches; however, <math alttext=\"x\"><mi>x</mi>\n</math> represents the length of the longer part of the wire, since it's given that the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math> more than <math alttext=\"4\"><mn>4</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>.</p>\n<p>Choice C is incorrect. This represents a part that is <math alttext=\"6\"><mn>6</mn>\n</math> more than the length of the other part, rather than <math alttext=\"6\"><mn>6</mn>\n</math> more than <math alttext=\"4\"><mn>4</mn>\n</math> times the length of the other part.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"25\"><mn>25</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"28\"><mn>28</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"56\"><mn>56</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"86\"><mn>86</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}