{"id":1696,"date":"2023-08-10T15:01:32","date_gmt":"2023-08-10T15:01:32","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=1696"},"modified":"2023-08-28T21:49:22","modified_gmt":"2023-08-28T21:49:22","slug":"psat-math-linear-word-problems","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-linear-word-problems\/","title":{"rendered":"PSAT Math: Linear Word Problems"},"content":{"rendered":"<p>On the PSAT Math Test, another way\u00a0linear equations can be made to look complicated is for them to be disguised in \u201creal-world\u201d word problems, where it\u2019s up to you to extract and solve an equation. When you\u2019re solving these PSAT math problems, you may run into trouble translating English into math. The following table shows some of the most common phrases and mathematical equivalents you\u2019re likely to see on the PSAT.<br \/>\u00a0<br \/><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-0  el_before_av_hr  avia-builder-el-first  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >PSAT Word Problems Translation Table<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><\/p>\n<div  style='height:10px' class='hr hr-invisible   avia-builder-el-1  el_after_av_heading  el_before_av_hr '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div>\n<p>\u00a0<\/p>\n<table cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td valign=\"middle\"><b>English<\/b><\/td>\n<td valign=\"middle\"><b>Math<\/b><\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>equals, is, equivalent to, was, will be, has, costs, adds up to, the same as, as much as<\/i><\/td>\n<td valign=\"middle\">=<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>times, of, multiplied by, product of, twice, double, by<\/i><\/td>\n<td valign=\"middle\">\u00d7<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>divided by, per, out of, each, ratio<\/i><\/td>\n<td valign=\"middle\">\u00f7<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>plus, added to, and, sum, combined, total, increased by<\/i><\/td>\n<td valign=\"middle\">+<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>minus, subtracted from, smaller than, less than, fewer, decreased by, difference between<\/i><\/td>\n<td valign=\"middle\">\u2013<\/td>\n<\/tr>\n<tr>\n<td valign=\"middle\"><i>a number, how much, how many, what<\/i><\/td>\n<td valign=\"middle\"><i>x, n,<\/i> etc.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div  style='height:10px' class='hr hr-invisible   avia-builder-el-2  el_after_av_hr  el_before_av_promobox '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div>\n<p>Linear word problems are made more difficult by complex phrasing and extraneous information. Don\u2019t get frustrated\u2014word problems can be broken down in predictable ways.<\/p>\n<p><br \/>To stay organized on Test Day, use the <b>Kaplan Strategy for Translating English into Math:<\/b><\/p>\n<ul>\n<li>Define any variables, choosing letters that make sense.<\/li>\n<li>Break sentences into short phrases.<\/li>\n<li>Translate each phrase into a mathematical expression.<\/li>\n<li>Put the expressions together to form an equation.<\/li>\n<\/ul>\n<p>Let\u2019s apply this to a straightforward example: Colin\u2019s age is three less than twice Jim\u2019s age.<\/p>\n<ul>\n<li><b><\/b>Define any variables, choosing letters that make sense: <em>We\u2019ll choose C for Colin\u2019s age and J for Jim\u2019s age.<\/em><\/li>\n<li><b><\/b>Break sentences into short phrases: <em>The information about Colin and the information about Jim seem like separate phrases.<\/em><\/li>\n<li><b><\/b>Translate each phrase into a mathematical expression: <em>Colin\u2019s age = C; 3 less than twice Jim\u2019s age = 2J \u2013 3.<\/em><\/li>\n<li><b><\/b>Put the expressions together to form an equation: <em>Combine the results to get C = 2J \u2013 3.<\/em><\/li>\n<\/ul>\n<p>This strategy fits into the larger framework of the Kaplan Method for Math: When you get to <b>Step 2: Choose the best strategy to answer the question<\/b> and are trying to solve a word problem as efficiently as possible, switch over to this strategy to move forward quickly.<\/p>\n<h3>PSAT Practice Question: Linear Word Problems<\/h3>\n<p>The Kaplan Strategy for Translating English into Math works every time. Apply it here to a test-like example:<\/p>\n\n\t<div  style='background:#ffffff;color:#333333;border-color:#cdcdcd;' class='av_promobox  avia-button-no   avia-builder-el-3  el_after_av_hr  avia-builder-el-last '>\t\t<div class='avia-promocontent'><p>\n1. A gym sells two types of one-year memberships. Package A costs $325 and includes an unlimited number of visits. Package B has a $185 enrollment fee, includes five free visits, and costs an additional $4 per visit after the first five. How many visits would a person need to use for Package B to cost the same amount as Package A?<\/p>\n<p>A. 30<br \/>\nB. 35<br \/>\nC. 40<br \/>\nD. 45<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-col-ffffff-background-color has-col-ffffff-color\"\/>\n\n\n\n<p>When translating from English to math, <em>start by defining the variables<\/em>, choosing letters that make sense. Then, <em>break the question down into small pieces<\/em>, writing down the translation for one phrase at a time.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>The phrase \u201chow many visits\u201d indicates an unknown, so you need a variable. Use an intuitive letter to represent the number of visits; call it <em>v<\/em>. The question asks when the two memberships will cost the \u201csame amount,\u201d so write an equation that sets the total membership costs equal to each other.<\/p>\n\n\n\n<p>Package A costs $325 for unlimited visits, so write 325 on one side of the equal sign. Package B costs $4 per visit (not including, or <em>except for<\/em>, the first 5 visits), or 4(<em>v <\/em>\u2212 5), plus a flat $185 enrollment fee, so write 4(<em>v <\/em>\u2212 5) + 185 on the other side of the equal sign. That\u2019s it! Now, solve for <em>v<\/em>:<\/p>\n\n\n\n<p class=\"has-text-align-center\">325 = 4(<em>v<\/em> \u2212 5) + 185 <\/p>\n\n\n\n<p class=\"has-text-align-center\">140 = 4<em>v <\/em>\u2212 20<\/p>\n\n\n\n<p class=\"has-text-align-center\">160 = 4<em>v<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\">40 = <em>v<\/em><\/p>\n\n\n\n<p>The answer is <strong>(C)<\/strong>.<\/p>\n\n\n\n<h3>On PSAT Test Day<\/h3>\n\n\n\n<p>PSAT word problems test your understanding of how to describe real-world situations using math equations. For some questions, it will be up to you to extract and solve an equation; for others, you\u2019ll have to interpret an equation in a real-world context.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-col-ffffff-background-color has-col-ffffff-color\"\/>\n\n\n\n<p>&lt;\u00a0<a href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-practice-questions-linear-equations\/\">Previous: PSAT Math Practice: Linear Equations<\/a><br>Next:\u00a0<a href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-linear-graphs\/\">PSAT Math: Linear Graphs ><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On the PSAT Math Test, another way\u00a0linear equations can be made to look complicated is for them to be disguised in \u201creal-world\u201d word problems, where it\u2019s up to you to extract and solve an equation. When you\u2019re solving these PSAT math problems, you may run into trouble translating English into math. The following table shows [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":44073,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1696"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=1696"}],"version-history":[{"count":24,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1696\/revisions"}],"predecessor-version":[{"id":44077,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1696\/revisions\/44077"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/44073"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=1696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=1696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=1696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}