{"id":"cb_question_bank:a6dd3223-7a74-4898-9ade-67dca60ea2a2","source_id":"cb_question_bank","source_item_id":"a6dd3223-7a74-4898-9ade-67dca60ea2a2","external_id":"cc329e0c-3593-4615-8425-0a35606bd546","ibn":null,"question_id":"0cadb20e","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f left parenthesis x right parenthesis equals StartFraction x plus 15 Over 5 EndFraction , and f left parenthesis a right parenthesis equals 10 , where a is a constant. What is the value of a ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals StartFraction x plus 15 Over 5 EndFraction\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mrow><mn>15</mn></mrow></mrow><mrow><mn>5</mn></mrow></mfrac></math>, and <math alttext=\"f left parenthesis a right parenthesis equals 10\"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mrow><mn>10</mn></mrow></math>, where <math alttext=\"a\"><mi>a</mi>\n</math> is a constant. What is the value of <math alttext=\"a\"><mi>a</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It's given that&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals StartFraction x plus 15 Over 5 EndFraction\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>15</mn></mrow><mn>5</mn></mfrac></math> and&nbsp;<math alttext=\"f left parenthesis a right parenthesis equals 10\"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>10</mn></math>, where <math alttext=\"a\"><mi>a</mi>\n</math> is a constant. Therefore, for the given function <math alttext=\"f\"><mi>f</mi>\n</math>, when <math alttext=\"x equals a\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mi>a</mi>\n</mrow>\n</math>,&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 10\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>10</mn></math>. Substituting <math alttext=\"a\"><mi>a</mi>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"10\"><mn>10</mn>\n</math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the given function <math alttext=\"f\"><mi>f</mi>\n</math> yields&nbsp;<math alttext=\"10 equals StartFraction a plus 15 Over 5 EndFraction\"><mn>10</mn><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>15</mn></mrow><mn>5</mn></mfrac></math>. Multiplying both sides of this equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields <math alttext=\"50 equals a plus 15\"><mn>50</mn><mo>=</mo><mi>a</mi><mo>+</mo><mn>15</mn></math>. Subtracting <math alttext=\"15\"><mn>15</mn>\n</math> from both sides of this equation yields <math alttext=\"35 equals a\"><mn>35</mn><mo>=</mo><mi>a</mi></math>. Therefore, the value of <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"35\"><mn>35</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the value of <math alttext=\"a\"><mi>a</mi>\n</math> if <math alttext=\"f left parenthesis a right parenthesis equals 4\"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>4</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the value of <math alttext=\"a\"><mi>a</mi>\n</math> if <math alttext=\"f left parenthesis a right parenthesis equals 5\"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>5</mn></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the value of <math alttext=\"a\"><mi>a</mi>\n</math> if <math alttext=\"f left parenthesis a right parenthesis equals 16\"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>16</mn></math>.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"35\"><mn>35</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"65\"><mn>65</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}}