{"id":"cb_practice_pdf:t10-math-m1-q26","source_id":"cb_practice_pdf","source_item_id":"t10-math-m1-q26","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-10","module_number":1,"position":26,"stem":"A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which function f gives the total cost, in ≥ 2 dollars, for x hours of repair, where x? = 60x+100","stimulus":"","stimulus_html":null,"stem_html":"<p>A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which function f gives the total cost, in ≥ 2 dollars, for x hours of repair, where x? = 60x+100</p>","rationale_html":"<p>$220 Choice A is correct. It’s given that the window repair specialist charges for the first two hours of repair plus an hourly fee for each additional hour. Let n represent the hourly fee for each additional hour after the first two hours. Since it’s given that x is the number of hours of repair, it follows that the charge generated by the hourly fee after the first two hours can be represented by the - expression n^x 2h. Therefore, the total cost, in dollars, for x hours of repair is =220+ -2 $400 f^xh n^x h. It’s given that the total cost for 5 hours of repair is . 400 =220+ -2 Substituting 5 for x and for f^xh into the equation f^xh n^x h 400=220+ 5-2 400=220+3 220 yields n^ h, or n. Subtracting from both sides 180=3 of this equation yields n. Dividing both sides of this equation by 3 yields =60 60 =220+ -2 n . Substituting for n in the equation f^xh n^x h yields =220+60 -2 =220+60 -120 f^xh ^x h, which is equivalent to f^xh x , or =60 +100 f^xh x . Therefore, the total cost, in dollars, for x hours of repair is =60 +100 f^xh x . Choice B is incorrect. This function represents the total cost, in dollars, for $340 $220 x hours of repair where the specialist charges , rather than , for the first two hours of repair. Choice C is incorrect. This function represents the total $160 cost, in dollars, for x hours of repair where the specialist charges , rather $220 $80 than , for the first two hours of repair, and an hourly fee of , rather than $60 , after the first two hours. Choice D is incorrect. This function represents the $380 total cost, in dollars, for x hours of repair where the specialist charges , $220 $80 rather than , for the first two hours of repair, and an hourly fee of , rather $60 than , after the first two hours.</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>f(x)</p>","ord":0},{"label":"B","content_html":"<p>f(x) = 60x+220</p>","ord":1},{"label":"C","content_html":"<p>f(x) = 80x</p>","ord":2},{"label":"D","content_html":"<p>f(x) = 80x+220 STO</p>","ord":3}],"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}}