{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-04-25T23:50:06+00:00","modifiedTime":"2017-04-25T23:50:06+00:00","timestamp":"2022-09-14T18:18:34+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"ACT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"},"slug":"act","categoryId":33775}],"title":"ACT Practice Math Questions: Working with Multiple Variables","strippedTitle":"act practice math questions: working with multiple variables","slug":"act-practice-math-questions-working-multiple-variables","canonicalUrl":"","seo":{"metaDescription":"As if one variable weren't enough, the ACT Math exam will sometimes throw multiple variables into some of its algebra questions. The following practice question","noIndex":0,"noFollow":0},"content":"As if one variable weren't enough, the ACT Math exam will sometimes throw multiple variables into some of its algebra questions. The following practice questions test your skills with using substitution to solve for the variables a and b, and rearranging an equation to solve it in terms of y – x.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>If a is five greater than b, and the sum of a and b is –15, then b2 =\r\n\r\nA. 100\r\nB. 64\r\nC. 25\r\nD. 20\r\nE. 0</li>\r\n\t<li>If\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1201.gif\"><img class=\"alignnone size-full wp-image-238587\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1201.gif\" alt=\"ACT_1201\" width=\"115\" height=\"47\" /></a>\r\nthen y – x =\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1202.gif\"><img class=\"alignnone size-medium wp-image-238588\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1202-95x255.gif\" alt=\"ACT_1202\" width=\"95\" height=\"255\" /></a></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is Choice (A).\r\n\r\nSet up equations from the wording of the question: a = 5 + b and a + b = –15. Substitute the value of a in the first equation for a in the second equation and solve for b:\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1203.gif\"><img class=\"alignnone size-full wp-image-238589\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1203.gif\" alt=\"ACT_1203\" width=\"115\" height=\"99\" /></a>\r\n\r\nSo b2 = 100.\r\n</li>\r\n\t<li>The correct answer is Choice (D).\r\n\r\nGet the terms that have y and x in them on one side and all the terms that have nothing to do with y and x on the other side:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1204.gif\"><img class=\"alignnone size-medium wp-image-238590\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1204-149x255.gif\" alt=\"ACT_1204\" width=\"149\" height=\"255\" /></a></li>\r\n</ol>","description":"As if one variable weren't enough, the ACT Math exam will sometimes throw multiple variables into some of its algebra questions. The following practice questions test your skills with using substitution to solve for the variables a and b, and rearranging an equation to solve it in terms of y – x.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>If a is five greater than b, and the sum of a and b is –15, then b2 =\r\n\r\nA. 100\r\nB. 64\r\nC. 25\r\nD. 20\r\nE. 0</li>\r\n\t<li>If\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1201.gif\"><img class=\"alignnone size-full wp-image-238587\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1201.gif\" alt=\"ACT_1201\" width=\"115\" height=\"47\" /></a>\r\nthen y – x =\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1202.gif\"><img class=\"alignnone size-medium wp-image-238588\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1202-95x255.gif\" alt=\"ACT_1202\" width=\"95\" height=\"255\" /></a></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is Choice (A).\r\n\r\nSet up equations from the wording of the question: a = 5 + b and a + b = –15. Substitute the value of a in the first equation for a in the second equation and solve for b:\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1203.gif\"><img class=\"alignnone size-full wp-image-238589\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1203.gif\" alt=\"ACT_1203\" width=\"115\" height=\"99\" /></a>\r\n\r\nSo b2 = 100.\r\n</li>\r\n\t<li>The correct answer is Choice (D).\r\n\r\nGet the terms that have y and x in them on one side and all the terms that have nothing to do with y and x on the other side:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1204.gif\"><img class=\"alignnone size-medium wp-image-238590\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1204-149x255.gif\" alt=\"ACT_1204\" width=\"149\" height=\"255\" /></a></li>\r\n</ol>","blurb":"","authors":[{"authorId":9086,"name":"Lisa Zimmer Hatch","slug":"lisa-zimmer-hatch","description":" Lisa Zimmer Hatch served as VP of The Center for Legal Studies, where she created standardized test preparation. Currently, she is an Independent College Counselor and president of College Primers. Scott A. Hatch develops courses for a variety of careers and assists those seeking advanced degrees in law, business, and other professions. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9086"}},{"authorId":9087,"name":"Scott A. Hatch","slug":"scott-a-hatch","description":" Lisa Zimmer Hatch served as VP of The Center for Legal Studies, where she created standardized test preparation. Currently, she is an Independent College Counselor and president of College Primers. Scott A. Hatch develops courses for a variety of careers and assists those seeking advanced degrees in law, business, and other professions. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9087"}}],"primaryCategoryTaxonomy":{"categoryId":33775,"title":"ACT","slug":"act","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":238694,"title":"ACT Practice Math Questions: Circles","slug":"act-practice-math-questions-circles","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/238694"}},{"articleId":238689,"title":"ACT Practice Math Questions: Interior Angles of a Polygon","slug":"act-practice-math-questions-interior-angles-polygon","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/238689"}},{"articleId":238684,"title":"ACT Practice Math Questions: Working with Angles","slug":"act-practice-math-questions-working-angles","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/238684"}},{"articleId":238681,"title":"ACT Practice Math Questions: Combinations and Permutations","slug":"act-practice-math-questions-combinations-permutations","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/238681"}},{"articleId":238678,"title":"ACT Practice Math Questions: Probability","slug":"act-practice-math-questions-probability","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/238678"}}],"fromCategory":[{"articleId":294142,"title":"ACT Prep 2023 For Dummies Cheat Sheet","slug":"act-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/294142"}},{"articleId":268046,"title":"How to Organize Your ACT Essay","slug":"how-to-organize-your-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268046"}},{"articleId":268043,"title":"How to Write a Great ACT Essay","slug":"how-to-write-a-great-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268043"}},{"articleId":268033,"title":"ACT Geometry Test: Triangle Trauma","slug":"act-geometry-test-triangle-trauma","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268033"}},{"articleId":268023,"title":"ACT Geometry Test: Analyzing Angles","slug":"act-geometry-test-analyzing-angles","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268023"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281910,"slug":"act-1001-practice-questions-for-dummies","isbn":"9781119275435","categoryList":["academics-the-arts","study-skills-test-prep","act"],"amazon":{"default":"https://www.amazon.com/gp/product/1119275431/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119275431/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119275431-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119275431/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119275431/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/act-1001-practice-questions-for-dummies-cover-9781119275435-204x255.jpg","width":204,"height":255},"title":"ACT","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"Lisa Zimmer Hatch, MA, and Scott A. 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ACT Practice Math Questions: Working with Multiple Variables

By: Lisa Zimmer Hatch and Scott A. Hatch and

Updated: 04-25-2017

From The Book: ACT

ACT

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As if one variable weren't enough, the ACT Math exam will sometimes throw multiple variables into some of its algebra questions. The following practice questions test your skills with using substitution to solve for the variables a and b, and rearranging an equation to solve it in terms of y – x.

Practice questions

If a is five greater than b, and the sum of a and b is –15, then b² =
A. 100 B. 64 C. 25 D. 20 E. 0
If
then y – x =

Answers and explanations

The correct answer is Choice (A).
Set up equations from the wording of the question: a = 5 + b and a + b = –15. Substitute the value of a in the first equation for a in the second equation and solve for b:
So b² = 100.
The correct answer is Choice (D).
Get the terms that have y and x in them on one side and all the terms that have nothing to do with y and x on the other side:

About This Article

This article is from the book:

ACT ,

About the book authors:

Lisa Zimmer Hatch, MA, and Scott A. Hatch, JD, have been helping students excel on standardized tests and navigate the college admissions process since 1987. They have written curricula and taught students internationally through live lectures, online forums, DVDs, and independent study.

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