{"id":"cb_question_bank:b413d193-119e-463b-a207-4659f18fe694","source_id":"cb_question_bank","source_item_id":"b413d193-119e-463b-a207-4659f18fe694","external_id":"cdc3a36c-aceb-4d6e-99f2-44a62cd1b9b1","ibn":null,"question_id":"2d54c272","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"5 upper G plus 45 upper R equals 380 At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won upper G green tokens and upper R red tokens worth a total of 380 points. The given equation represents this situation. How many more points is a red token worth than a green token?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"5 upper G plus 45 upper R equals 380\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>5</mn>\n\t\t\t<mi>G</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>45</mn>\n\t\t\t<mi>R</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>380</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won <math alttext=\"upper G\"><mi>G</mi>\n</math> green tokens and <math alttext=\"upper R\"><mi>R</mi>\n</math> red tokens worth a total of <math alttext=\"380\"><mn>380</mn>\n</math> points. The given equation represents this situation. How many more points is a red token worth than a green token?</p>","rationale_html":"<p>The correct answer is <math alttext=\"40\"><mn>40</mn>\n</math>. It's given that <math alttext=\"5 upper G plus 45 upper R equals 380\"><mn>5</mn><mi>G</mi><mo>+</mo><mn>45</mn><mi>R</mi><mo>=</mo><mn>380</mn></math>, where <math alttext=\"upper G\"><mi>G</mi>\n</math> is the number of green tokens and <math alttext=\"upper R\"><mi>R</mi>\n</math> is the number of red tokens won by one student and these tokens are worth a total of <math alttext=\"380\"><mn>380</mn>\n</math> points. Since the equation represents the situation where the student won points with green tokens and red tokens for a total of <math alttext=\"380\"><mn>380</mn>\n</math> points, each term on the left-hand side of the equation represents the number of points won for one of the colors. Since the coefficient of <math alttext=\"upper G\"><mi>G</mi>\n</math> in the given equation is <math alttext=\"5\"><mn>5</mn>\n</math>, a green token must be worth <math alttext=\"5\"><mn>5</mn>\n</math> points. Similarly, since the coefficient of <math alttext=\"upper R\"><mi>R</mi>\n</math> in the given equation is <math alttext=\"45\"><mn>45</mn>\n</math>, a red token must be worth <math alttext=\"45\"><mn>45</mn>\n</math> points. Therefore, a red token is worth <math alttext=\"45 minus 5\"><mn>45</mn><mo>-</mo><mn>5</mn></math> points, or <math alttext=\"40\"><mn>40</mn>\n</math> points, more than a green token.</p>","correct_answer":["40"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.814000+00:00","source_updated_at":"2023-08-02T20:25:59.814000+00:00","options":[],"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}}