{"id":"act_practice_pdf:pt1:math:020","source_id":"act_practice_pdf","source_item_id":"pt1-math-020","external_id":null,"program":"ACT","section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":"G","subcategory":"Geometry","form_id":"act_practice_pdf:pt1","passage_id":null,"position":20,"scored":true,"layout_warning":null,"stem":"At a certain time of day, a flagpole casts a 9.0 -foot-long shadow and a nearby 4.0 -foot-tall fence post casts a 2.4 -foot-long shadow. Given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?","stimulus":"","stimulus_html":"
\"Question
As printed in the official booklet.
","stem_html":"

At a certain time of day, a flagpole casts a 9.0 -foot-long shadow and a nearby 4.0 -foot-tall fence post casts a 2.4 -foot-long shadow. Given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?

","rationale_html":null,"correct_answer":["H"],"equiv_key":"647ecd77eca90cde51307d15","has_media":true,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"

5.4

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

10.6

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

15.0

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

15.4

","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:q3:06","source_id":"act_quizme","source_item_id":"math-q3-06","external_id":"64208b599b993697","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":6,"scored":true,"layout_warning":null,"stem":"At a certain time of day, a flagpole casts a 9.0-foot-long shadow and a nearby 4.0-foot-tall fence post casts a 2.4-foot-long shadow. Given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?","stimulus":"","stimulus_html":null,"stem_html":"
\t\t\t\t\t \t\t\t\t\t

At a certain time of day, a flagpole casts a 9.0-foot-long shadow and a nearby 4.0-foot-tall fence post casts a 2.4-foot-long shadow. Given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?

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

F. Incorrect. The flagpole height, x, and its shadow length are proportional to the fence post height and its shadow length. When you are setting up the proportion, be sure to create fractions that relate the corresponding parts of each object. You may have set up x9.0=2.44.0 and solved for x=2.44.09.0.

G. Incorrect. The flagpole height, x, and its shadow length are proportional to the fence post height and its shadow length. Try setting up a proportion using fractions that relate the corresponding parts of each object. You may have calculated 9.0+4.0-2.4.

H. Correct. The flagpole height and its shadow length are proportional to the fence post height and its shadow length. Let x represent the flagpole height and set up the proportional relationship equation x4.0=9.02.4. Then, multiply both sides of the equation by 4.0 to calculate the height of the flagpole: x=9.02.44.0=15.0.

J. Incorrect. The flagpole height, x, and its shadow length are proportional to the fence post height and its shadow length. Try setting up a proportion with fractions that relate the corresponding parts of each object. You may have simply added all the given values: 9.0+2.4+4.0.

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