{"id":"act_practice_pdf:pt2:math:018","source_id":"act_practice_pdf","source_item_id":"pt2-math-018","external_id":null,"program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":"act_practice_pdf:pt2","passage_id":null,"position":18,"scored":false,"layout_warning":null,"stem":"The sum of 3 positive integers is 180 , and the ratio of the integers is 5:3:2 . What is the value of the smallest of the integers?","stimulus":"","stimulus_html":"
\"Question
As printed in the official booklet.
","stem_html":"

The sum of 3 positive integers is 180 , and the ratio of the integers is 5:3:2 . What is the value of the smallest of the integers?

","rationale_html":null,"correct_answer":["G"],"equiv_key":"5a1164d4d54633c807531f9d","has_media":true,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"

18

","ord":0},{"label":"G","content_html":"

36

","ord":1},{"label":"H","content_html":"

54

","ord":2},{"label":"J","content_html":"

90

","ord":3}],"passage":null,"attribution":{"source_id":"act_practice_pdf","source_name":"Official ACT full-length practice tests (PDF)","rights_holder":"ACT Education Corp.","canonical_url":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","retrieved_from":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","attribution":"Full-length ACT practice tests © ACT Education Corp., published free at act.org. Questions are retired items from previous ACT administrations.","disclaimer":"Extracted from a print-layout PDF: equations, figures and charts do not survive as text. Use the original PDF for anything that renders poorly. ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free for personal test preparation; not licensed for redistribution.","redistributable":false,"item_count":342},"equivalents":[{"id":"act_quizme:math:q3:02","source_id":"act_quizme","source_item_id":"math-q3-02","external_id":"0ad1a0231330a448","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":2,"scored":true,"layout_warning":null,"stem":"The sum of 3 positive integers is 180, and the ratio of the integers is 5 to 3 to 2 5 : 3 : 2 . What is the value of the smallest of the integers?","stimulus":"","stimulus_html":null,"stem_html":"
\t\t\t\t\t \t\t\t\t\t

The sum of 3 positive integers is 180, and the ratio of the integers is 5 to 3 to 25:3:2. What is the value of the smallest of the integers?

\t\t\t\t
\t\t\t\t
\n
","rationale_html":"

F. Incorrect. Since you are given that the ratio of the integers is 5:3:2, try writing the 3 integers in terms of a variable, x: n1=5x, n2=3x, and n3=2x. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You might have solved for x and stopped.

G. Correct. Since you are given that the ratio of the integers is 5:3:2, write the 3 integers in terms of a variable, x: n1=5x, n2=3x, and n3=2x. Because the sum of these 3 integers is 180, set up the equation 5x+3x+2x=180. Then, solve the equation for x, resulting in x=18. Finally, substitute 18 for x to calculate the smallest integer: n3=2x=218=36.

H. Incorrect. Since you are given that the ratio of the integers is 5:3:2, try writing the 3 integers in terms of a variable, x: n1=5x, n2=3x, and n3=2x. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You might have solved for x but then calculated n2 instead of n3: n2=318=54.

J. Incorrect. Since you are given that the ratio of the integers is 5:3:2, try writing the 3 integers in terms of a variable, x: n1=5x, n2=3x, and n3=2x. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You may have solved for x but then calculated n1 instead of n3: n1=5(18)=90.

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