{"id":2252,"date":"2022-12-05T10:50:02","date_gmt":"2022-12-05T10:50:02","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=2252"},"modified":"2022-12-05T21:40:25","modified_gmt":"2022-12-05T21:40:25","slug":"psat-math-quiz-equations-and-word-problems","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-quiz-equations-and-word-problems\/","title":{"rendered":"PSAT Math Quiz: Equations and Word Problems"},"content":{"rendered":"<p>Content Review:<\/p>\n<ul>\n<li><a title=\"PSAT Math Strategies and Linear Equations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-strategies-and-linear-equations\/\">PSAT Math: Math Strategies and Linear Equations<\/a><\/li>\n<li><a title=\"PSAT Math Practice Questions: Linear Equations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-practice-questions-linear-equations\/\">PSAT Math: Linear Equations Practice Question<\/a>s<\/li>\n<li><a title=\"PSAT Math: Linear Word Problems\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-linear-word-problems\/\">PSAT Math: Linear Word Problems<\/a><\/li>\n<li><a title=\"PSAT Math: Linear Graphs\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-linear-graphs\/\">PSAT Math: Linear Graphs<\/a><\/li>\n<\/ul>\n<p>Test your <a title=\"psat math\" href=\"https:\/\/www.kaptest.com\/psat\">PSAT readiness<\/a> by taking this PSAT Math quiz!<br \/>\n<div  class='avia-builder-widget-area clearfix  avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '><div id=\"custom_html-34\" class=\"widget_text widget clearfix widget_custom_html\"><div class=\"textwidget custom-html-widget\"><div><div class='op-interactive' id='638e2b22889b9a59e26e85d1' data-title='PSAT Math Quiz: Linear Equations' data-url='https:\/\/kaplannorthamerica.outgrow.us\/638e2b22889b9a59e26e85d1?vHeight=1' data-width='100%'><\/div><script src='\/\/dyv6f9ner1ir9.cloudfront.net\/assets\/js\/nloader.js'><\/script><script>initIframe('638e2b22889b9a59e26e85d1');<\/script><\/div><\/div><\/div><\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_sidebar  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><\/p>\n<p><strong>Question 1<\/strong><\/p>\n<p>-2 (x &#8211; 3) = 17. Solve for x.<\/p>\n<section class=\"QuizQuestion-info\">\n<article class=\"QuizQuestion-info-description-container\">\n<div><\/div>\n<div class=\"QuizQuestion-info-description\">A. -22\/3<br \/>\nB. -10<br \/>\nC. -7<br \/>\nD. -11\/2<\/div>\n<\/article>\n<\/section>\n<p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-2  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Answer 1<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><b>D:&nbsp;<\/b>Straightforward math works well on simple equations like this one. Start by carefully distributing the -1 on the left. Then combine like terms and divide by -2 on both sides to isolate <i>x<\/i>. You should find that&nbsp;<em>x&nbsp;<\/em>= -11\/2, which is (D).<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-3  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>Question 2<\/strong><\/p>\n<p>Jacques Charles was a French scientist who discovered the relationship between the&nbsp;temperature and volume of a gas. Specifically, Charles found that gases expand when&nbsp;heated. This relationship was formalized in Charles\u2019s Law, which illustrates a linear&nbsp;relationship between temperature and volume in gases.<\/p>\n<p>The graph here shows the&nbsp;volume of a sample of gas as it is cooled. If T is the temperature of the gas in \u00b0C and V&nbsp;is the volume in liters, which of the following equations, when plotted, could produce&nbsp;the graph shown?<br \/>\n<a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-7.58.31-PM.png\"><img loading=\"lazy\" class=\"alignnone size-medium wp-image-26025\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-7.58.31-PM-300x168.png\" alt=\"psat math\" width=\"300\" height=\"168\"><\/a><br \/>\nA. V = 0.004T + 100<br \/>\nB. V = 0.004T<br \/>\nC. V = 0.004T + 1<br \/>\nD. V = 0.004T &#8211; 0.25<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-4  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-2\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-2\">Answer 2<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-2\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>C:&nbsp;<\/strong>Don&#8217;t get bogged down by the prose; focus on what you need to answer the question posed. Temperature (<em>T<\/em>) is the independent variable on the&nbsp;<em>x<\/em>-axis, and volume (<em>V<\/em>) is the dependent variable on the&nbsp;<em>y<\/em>-axis. Therefore, the skeleton of the equation you&#8217;re looking for is&nbsp;<em>V = mT + b.<\/em><\/p>\n<p>Because each answer choice has a different&nbsp;<em>y-<\/em>intercept, finding this is enough to get you to the right answer; there is no need to determine the slope. Although the graph is not centered like you&#8217;re used to, you can still find the&nbsp;<em>y<\/em>-intercept. In this case, it&#8217;s 1. This eliminates every answer choice except (C), which is correct.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-5  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>Question 3<\/strong><\/p>\n<p>Ms. Walser\u2019s class had 18 students. She used three equally weighted tests to determine&nbsp;their final grades. The class average for the first test was 92, and the class average for the second test was 77. If the overall class average was 84, what was the average score&nbsp;for the third test?<\/p>\n<p>A. 74.3<br \/>\nB. 77<br \/>\nC. 83<br \/>\nD. 84.3<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-6  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-3\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-3\">Answer 3<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-3\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>C:&nbsp;<\/strong>The Kaplan Strategy for Translating English into Math will work well here. Watch out for extra information that may confuse you. Let&nbsp;<em>a<\/em> be the average of Test One (92);&nbsp;<em>b,&nbsp;<\/em>the average of Test Two (77);&nbsp;<em>c,&nbsp;<\/em>the average of Test Three (what you need to find); and&nbsp;<em>d,&nbsp;<\/em>the overall test average (84).<\/p>\n<p>The average is the sum of the terms divided by the number of terms: (a + b + c) \/ 3 = d. Plugging in the values you know yields (92 + 77 + c) \/ 3 = 84. Multiply both sides by 3 and then subtract to solve for&nbsp;<em>c,&nbsp;<\/em>which gives 83. This corresponds to (C).<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-7  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>Question 4<\/strong><\/p>\n<p>A certain gym sells two membership packages. The first package, the Die-Hard Package, costs $250 for 6 months of unlimited use. The second package, the Personal Package, costs $130 initially plus $4 each day the member visits. How many visits would a person need to use for each package to cost the same amount over a 6-month period?<\/p>\n<p>A. 2<br \/>\nB. 20<br \/>\nC. 96<br \/>\nD. 120<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-8  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-4\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-4\">Answer 4<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-4\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><b>B:&nbsp;<\/b>Follow the Kaplan Strategy for Translating English into Math. Assemble equations and set them equal to each other. Let&nbsp;<em>d&nbsp;<\/em>= Die-Hard Package,&nbsp;<em>p =&nbsp;<\/em>Personal Package, and&nbsp;<em>v<\/em> = number of visits. Using the information about each package, you know that&nbsp;<em>d<\/em> = 250 and <i>p<\/i> = 130 + 4<i>v.&nbsp;<\/i><\/p>\n<p>Now, solve for&nbsp;<em>v<\/em>:<br \/>\n250 = 130 + 4v<br \/>\n120 + 4v<br \/>\n30 = v<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-9  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>Question 5<\/strong><\/p>\n<p>A municipality charges two types of local taxes: a per capita tax, which is a flat fee that every person pays, and a local income tax, which is a percentage of the person\u2019s annual income,&nbsp;<i>i<\/i>. If a taxpayer\u2019s total tax bill is given by the function&nbsp;<i>T<\/i>&nbsp;= 0.02<i>i<\/i>&nbsp;+ 25, then the value 0.02 best represents which of the following?<\/p>\n<p>A. The per capita tax<br \/>\nB. The taxpayer&#8217;s annual income<br \/>\nC. The total&nbsp;tax bill minus the per capita tax<br \/>\nD. The amount of the income tax as a percentage<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-10  el_after_av_promobox  avia-builder-el-last \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-5\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-5\">Answer 5<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-5\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p>The total bill consists of a flat tax and a percentage of annual income. The flat per capita tax is a one-time fee that does not depend on the taxpayer&#8217;s income and therefore should not be multiplied by&nbsp;<em>i.<\/em> This means that 25 is the per capita tax. The other expression in the equation, 0.02<em>i,<\/em> represents the percentage income tax times the annual income (which the question tells you is&nbsp;<em>i<\/em>). Therefore, 0.02 must represent the amount of the income tax as a percentage, which is (D).<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><\/p>\n<p>Next: <a title=\"PSAT Math Quiz: Systems of Equations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-systems-of-equations\/\">PSAT Math Quiz: Systems of Equations<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Content Review: PSAT Math: Math Strategies and Linear Equations PSAT Math: Linear Equations Practice Questions PSAT Math: Linear Word Problems PSAT Math: Linear Graphs Test your PSAT readiness by taking this PSAT Math quiz! Next: PSAT Math Quiz: Systems of Equations<\/p>\n","protected":false},"author":1,"featured_media":42035,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[195,310,311],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2252"}],"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=2252"}],"version-history":[{"count":7,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2252\/revisions"}],"predecessor-version":[{"id":42036,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2252\/revisions\/42036"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/42035"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=2252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=2252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=2252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}