A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?
","rationale_html":"The correct answer is 5. Let x represent the width, in inches, of the rectangle. It’s given that the length of the rectangle is 4 inches less than 7 times its width, or 7 -4 x inches. The area of a rectangle is equal to its width multiplied by its length. 7 -4 7 -4 Multiplying the width, x inches, by the length, x inches, yields x^ x h 155 square inches. It’s given that the rectangle has an area of square inches, so it 7 -4 =155 7 2-4 =155 155 follows that x^ x h , or x x . Subtracting from both sides 7 2-4 -155=0 of this equation yields x x . Factoring the left-hand side of this 7 +31 -5 =0 equation yields ^ x h^x h . Applying the zero product property to this 31 =- = equation yields two solutions: x 7 and x 5. Since x is the rectangle’s width, in inches, which must be positive, the value of x is 5. Therefore, the width of the rectangle, in inches, is 5.
","correct_answer":["5"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}