{"id":7299,"date":"2014-07-23T16:57:12","date_gmt":"2014-07-23T16:57:12","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7299"},"modified":"2014-12-02T08:25:27","modified_gmt":"2014-12-02T08:25:27","slug":"math-review-of-changing-application-problems-into-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-changing-application-problems-into-equations\/","title":{"rendered":"Math Review of Changing Application Problems into Equations"},"content":{"rendered":"

Overview<\/h3>\n

The first step in solving real-world problems mathematically is to change the problem into an equation. Sometimes, it is a matter of deciding what operations need to be used. It is also a matter of seeing how quantities relate to one another.<\/p>\n

Operations<\/h3>\n

Words and phrases that represent addition include such things as added to, increased from, more than, or the sum of. For example, 9 added to a number could be represented algebraically as 9 + x. \u00a0Words and phrases that represent subtraction include, subtracted from, less than, decreased by, or the difference between. Statements such as multiplied by, the product of, twice or three times, or a certain percent indicate multiplication, and statements such as divided by or the quotient of can indicate division. Sometimes a statement can indicate more than one operation. For example, a statement such as 5 less than 3 times a number could be represented as 3x – 5.<\/p>\n

Figure 1: Some words that suggest mathematical operations.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Relationships<\/h3>\n

It is also important to determine the relationship between quantities. Suppose that the length of a rectangle is 5 inches longer than its width. The width of the rectangle could be represented as w, so the length is w + 5. When one quantity is given in terms of another, it is usually easier to let one variable stand for the base amount. Any letter other than x can be used, as long as what the variable stands for is clearly defined.<\/p>\n

Using Multiplication<\/h3>\n

Suppose that one notebook costs $3.00. Then 5 notebooks would cost 5 \u2219 3 or $15.00. If one textbook costs x, then 5 copies of the same text would cost 5x. Similarly, the cost of x items at y dollars can be represented as xy. Sometimes a statement can include more than one operation. Suppose the cost to rent a truck included a daily fee of $40.00, as well as a mileage fee of 60 cents a mile.\u00a0If the truck were being rented for 2 days, the total cost of the truck would be the daily fee of 40.00 \u2219 2 for the number of days, plus the mileage fee of 0.60x.<\/p>\n

Figure 2: Using multiplication and addition to solve a problem.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Translating Applications into Equations<\/h3>\n

The word is often means is equal to. Suppose in the truck rental example, the total cost of the truck rental is $260.00. Then $80.00 + 0.60x = 260.00. The equation could then be solved as .60x = 260 – 80, or .60x = 180, or x = 180\/.60 = 300 miles.<\/p>\n

Figure 3: An example of translating an application to an equation.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Sioux City, IA: visit Tutoring in Sioux City, IA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview The first step in solving real-world problems mathematically is to change the problem into an equation. Sometimes, it is a matter of deciding what operations need to be used. It is also a matter of seeing how quantities relate to one another. Operations Words and phrases that represent addition include such things as added […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2772,2771],"class_list":["post-7299","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-relationship-between-quantities","tag-translating-applications-into-equations"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=7299"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7299\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}