{"id":217,"date":"2023-01-30T16:40:06","date_gmt":"2023-01-30T16:40:06","guid":{"rendered":"https:\/\/cwassignments.com\/blog\/?p=217"},"modified":"2024-05-10T07:51:12","modified_gmt":"2024-05-10T07:51:12","slug":"general-word-problems","status":"publish","type":"post","link":"https:\/\/cwassignments.com\/blog\/general-word-problems\/","title":{"rendered":"General Word Problems"},"content":{"rendered":"<h3>General Strategy<\/h3>\n<p style=\"font-weight: 400;\">Recall the general strategy for setting up word problems. Refer to the Problem Solving Strategies page for more detail.<\/p>\n<ol>\n<li style=\"font-weight: 400;\">Read the problem carefully: Determine what is known, what is unknown, and what question is being asked.<\/li>\n<li style=\"font-weight: 400;\">Represent unknown quantities in terms of a variable.<\/li>\n<li style=\"font-weight: 400;\">Use diagrams where appropriate.<\/li>\n<li style=\"font-weight: 400;\">Find formulas or mathematical relationships between the knowns and the unknowns.<\/li>\n<li style=\"font-weight: 400;\">Solve the equations for the unknowns.<\/li>\n<li style=\"font-weight: 400;\">Check answers to see if they are reasonable.<\/li>\n<\/ol>\n<h3>Number\/Geometry Problems<\/h3>\n<p style=\"font-weight: 400;\"><b><strong>Example:<\/strong><\/b>\u00a0 Find a number such that 5 more than one-half the number is three times the number.<\/p>\n<table style=\"font-weight: 400;\" width=\"377\">\n<tbody>\n<tr>\n<td width=\"56%\">Let\u00a0<em>x<\/em>\u00a0be the unknown number.<\/td>\n<td width=\"43%\"><\/td>\n<\/tr>\n<tr>\n<td width=\"56%\">Translating into math:<\/td>\n<td width=\"43%\">5\u00a0+\u00a0<em>x<\/em>\/2\u00a0=\u00a03<em>x<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"56%\">Solving: (First multiply by 2 to clear the fraction)<\/td>\n<td width=\"43%\">5\u00a0+\u00a0<em>x<\/em>\/2\u00a0=\u00a03<em>x<br \/>\n<\/em>10\u00a0+\u00a0<em>x<\/em>\u00a0=\u00a06<em>x<\/em><br \/>\n10\u00a0=\u00a05<em>x<\/em><br \/>\n<em>x<\/em>\u00a0=\u00a02<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\"><b><strong>Example:<\/strong><\/b>\u00a0If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides?<\/p>\n<p style=\"font-weight: 400;\">Let one side be\u00a0<em>x<\/em>\u00a0and the other side be\u00a0<em>x<\/em>\u00a0+\u00a01.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-219\" src=\"https:\/\/cwassignments.com\/blog\/wp-content\/uploads\/2023\/01\/image002.gif\" alt=\"general-word-problems\" width=\"157\" height=\"147\" \/><\/p>\n<p style=\"font-weight: 400;\">Then the given condition may be expressed as<\/p>\n<p style=\"font-weight: 400;\"><em>x<\/em>\u00a0+\u00a0<em>x<\/em>\u00a0+\u00a0(<em>x<\/em>\u00a0+\u00a01)\u00a0+\u00a0(<em>x<\/em>\u00a0+\u00a01)\u00a0=\u00a010<\/p>\n<p style=\"font-weight: 400;\">Solving:<\/p>\n<p style=\"font-weight: 400;\">4<em>x<\/em>\u00a0+\u00a02\u00a0=\u00a010<br \/>\n4<em>x<\/em>\u00a0=\u00a08<br \/>\n<em>x<\/em>\u00a0=\u00a02<\/p>\n<p style=\"font-weight: 400;\">so the sides have length\u00a0<b><strong>2 and 3<\/strong><\/b>.<\/p>\n<h3>Rate-Time Problems<\/h3>\n<ul>\n<li style=\"font-weight: 400;\">Rate\u00a0=\u00a0Quantity\/Time<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">or<\/p>\n<ul>\n<li style=\"font-weight: 400;\">Quantity = Rate \u00d7 Time<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\"><b><strong>Example:<\/strong><\/b>\u00a0 A fast employee can assemble 7 radios in an hour, and another slower employee can only assemble 5 radios per hour. If both employees work together, how long will it take to assemble 26 radios?<\/p>\n<p style=\"font-weight: 400;\">The two together will build 7 + 5 = 12 radios in an hour, so their combined rate is 12 radios\/hr.<\/p>\n<p style=\"font-weight: 400;\">Using Time = Quantity\/Rate, Time\u00a0=\u00a026\/12\u00a0=\u00a02\u00a01\/6\u00a0h or\u00a0<b><strong>2 hours 10 minutes<\/strong><\/b><\/p>\n<p style=\"font-weight: 400;\"><b><strong>Example:<\/strong><\/b>\u00a0 you are driving along at 55 mph when you are passed by a car doing 85 mph. How long will it take for the car that passed you to be one mile ahead of you?<\/p>\n<p style=\"font-weight: 400;\">We know the two rates, and we know that the difference between the two distances traveled will be one mile, but we don\u2019t know the actual distances. Let\u00a0<em>D\u00a0<\/em>be the distance that you travel in time\u00a0<em>t<\/em>, and\u00a0<em>D<\/em>\u00a0+ 1 be the distance that the other car traveled in time\u00a0<em>t<\/em>. Using the rate equation in the form\u00a0<em>distance\u00a0=\u00a0speed\u00a0<\/em>\u2022<em>\u00a0time\u00a0<\/em>for each car we can write<\/p>\n<p style=\"font-weight: 400;\">D\u00a0=\u00a055\u00a0<em>t<\/em>, and\u00a0<em>D<\/em>\u00a0+\u00a01\u00a0=\u00a085\u00a0<em>t<\/em><\/p>\n<p style=\"font-weight: 400;\">Substituting the first equation into the second,<\/p>\n<p style=\"font-weight: 400;\">55<em>t<\/em>\u00a0+\u00a01\u00a0=\u00a085<em>t\u00a0<\/em>\u201330<em>t<\/em>\u00a0=\u00a0\u20131<br \/>\n<em>t<\/em>\u00a0=\u00a01\/30\u00a0hr(or\u00a0<b><strong>2 minutes<\/strong><\/b>)<\/p>\n<h3>Mixture Problems<\/h3>\n<p style=\"font-weight: 400;\"><b><strong>Example:<\/strong><\/b>\u00a0 How much of a 10% vinegar solution should be added to 2 cups of a 30% vinegar solution to make a 20% solution?<\/p>\n<p style=\"font-weight: 400;\">Let\u00a0<em>x<\/em>\u00a0be the unknown amount of 10% solution. Write an equation for the amount of vinegar in each mixture:<\/p>\n<p style=\"font-weight: 400;\">(amount of vinegar in first solution) + (amount of vinegar in second solution) = (amount of vinegar in total solution)<\/p>\n<p style=\"font-weight: 400;\">0.1<em>x<\/em>\u00a0+\u00a00.3(2)\u00a0=\u00a00.2(<em>x<\/em>\u00a0+\u00a02)<\/p>\n<p style=\"font-weight: 400;\">0.1<em>x<\/em>\u00a0+\u00a00.6\u00a0=\u00a00.2<em>x<\/em>\u00a0+\u00a00.4<\/p>\n<p style=\"font-weight: 400;\">\u20130.1<em>x<\/em>\u00a0=\u00a0\u20130.2<\/p>\n<p style=\"font-weight: 400;\"><em>x<\/em>\u00a0=\u00a0<b><strong>2 cups<\/strong><\/b><\/p>\n<p>Troubled by &#8220;General Word Problems&#8221; in your math course? Secure <a href=\"https:\/\/cwassignments.com\/assignment-help.html\">expert assignment help<\/a> to solve them with ease and confidence!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>General Strategy Recall the general strategy for setting up word problems. Refer to the Problem Solving Strategies page for more detail. Read the problem carefully: Determine what is known, what is unknown, and what question is being asked. Represent unknown quantities in terms of a variable. Use diagrams where appropriate. Find formulas or mathematical relationships [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":698,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"_swt_meta_header_display":false,"_swt_meta_footer_display":false,"_swt_meta_site_title_display":false,"_swt_meta_sticky_header":false,"_swt_meta_transparent_header":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-217","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-algebra"],"_links":{"self":[{"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/posts\/217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/comments?post=217"}],"version-history":[{"count":4,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/posts\/217\/revisions"}],"predecessor-version":[{"id":530,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/posts\/217\/revisions\/530"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/media\/698"}],"wp:attachment":[{"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/media?parent=217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/categories?post=217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cwassignments.com\/blog\/wp-json\/wp\/v2\/tags?post=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}