{"id":1801,"date":"2019-08-24T12:43:33","date_gmt":"2019-08-24T17:43:33","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=1801"},"modified":"2023-08-29T15:19:42","modified_gmt":"2023-08-29T15:19:42","slug":"psat-math-practice-word-problems-multiple-equations","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-practice-word-problems-multiple-equations\/","title":{"rendered":"PSAT Math Practice: Word Problems & Multiple Equations"},"content":{"rendered":"

While solving systems of equations can be relatively straightforward once you get the hang of it, sometimes you’ll encounter a complex word problem and need to translate it into a system of equations and then solve. It sounds a lot scarier than it actually is. Remember to use the Kaplan Strategy for Translating English into Math to set up your equations, and then solve using either substitution or combination.
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PSAT Math Practice Question: Word Problems with Multiple Equations<\/h3>
<\/div><\/div><\/div>
\n\t
\t\t

\nAt a snack stand, hot dogs cost $3.50 and hamburgers cost $5. If the snack stand sold 27 snacks and made $118.50 in revenue, how many hot dogs were sold? How many hamburgers?<\/p>\n

A. 16 hot dogs; 11 hamburgers
\nB. 16 hot dogs; 16 hamburgers
\nC. 11 hot dogs; 14 hamburgers
\nD. 11 hot dogs; 16 hamburgers<\/p>\n<\/div><\/div><\/p>\n

<\/span><\/span><\/div>\n

Work through \u00a0the Kaplan Method for Math to solve this question\u00a0step-by-step. The following table shows Kaplan\u2019s strategic thinking on the left, along with suggested math scratchwork on the right.<\/p>\n

\n\n\n\n\n\n\n\n
Strategic Thinking<\/th>\nMath Scratchwork<\/th>\n<\/tr>\n<\/thead>\n
Step 1: Read the question, identifying and organizing important information as you go<\/b><\/p>\n

You need to find the number of hot dogs and hamburgers sold.<\/td>\n

<\/td>\n<\/tr>\n
Step 2: Choose the best strategy to answer the question<\/b><\/p>\n

Use the Kaplan Strategy for Translating English into Math.<\/p>\n

What variables should you use?<\/i><\/strong><\/p>\n

Because both snacks start with h<\/i>, that\u2019s likely to be a confusing choice. Instead, use d<\/i> for hot dogs and b<\/i> for hamburgers.<\/p>\n

How do you break apart the question into smaller phrases?<\/i><\/strong><\/p>\n

Break off each piece of relevant information into a separate phrase.<\/p>\n

What should you do with the phrases?<\/i><\/strong><\/p>\n

Translating each phrase into a math expression will create the components of a system of equations.<\/p>\n

What is the system of equations that will get you to the answer?<\/i><\/strong><\/p>\n

Assemble the math expressions you have to get the system of equations needed.<\/p>\n

How can you best solve this system of equations?<\/i><\/strong><\/p>\n

In this case, you can use either substitution or combination to arrive at the numbers of hot dogs and hamburgers. To use combination, multiply the first equation by \u20135 to set it up:<\/p>\n

Continuing to solve, you see that d<\/i> = 11.<\/span><\/p>\n

What does this information enable you to do?<\/i><\/strong><\/p>\n

That immediately eliminates A and B. You can plug 11 back into the first equation to get b.<\/i><\/td>\n

\nd<\/i> = hot dogs sold b<\/i> = hamburgers sold<\/p>\n

hot dogs cost $3.50 \u2192 3.5d <\/i><\/p>\n

hamburgers cost $5 \u2192 5b <\/i><\/p>\n

snack stand sold 27 snacks \u2192 d<\/i> + b<\/i> = 27<\/p>\n

made $118.50 in revenue \u2192 Total $ = 118.5
\n d<\/i> + b<\/i> = 27 3.5d<\/i> + 5b<\/i> = 118.5<\/p>\n

\u22125d<\/em> \u2212 5b<\/em> = \u2212135 + 3.5d + 5b = 118.5 \u22121.5d<\/em> + 0b<\/em> = \u221216.5<\/p>\n

d<\/em>\u00a0=\u00a011<\/p>\n

d<\/i> + b<\/i> = 27<\/p>\n

11 + b<\/i> = 27<\/p>\n

b<\/i> = 16<\/td>\n<\/tr>\n

Step 3: Check that you answered the<\/b> right<\/i><\/b> question<\/b><\/p>\n

The only answer choice that meets these criteria is (D).<\/td>\n

<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Always choose variable names that make sense to you. Countless students struggle on multi-part\u00a0problems due to disorganized notes. Don\u2019t let that happen to you. Move beyond\u00a0x<\/b><\/i>\u00a0and\u00a0y<\/b><\/i> when selecting variable names.<\/p>\n

Other questions of this type will simply ask you to choose from a series of answer choices that describes the system of equations\u2014they won\u2019t actually ask you to calculate a solution! These questions can be great time-savers.<\/p>\n","protected":false},"excerpt":{"rendered":"

While solving systems of equations can be relatively straightforward once you get the hang of it, sometimes you’ll encounter a complex word problem and need to translate it into a system of equations and then solve. It sounds a lot scarier than it actually is. Remember to use the Kaplan Strategy for Translating English into […]<\/p>\n","protected":false},"author":1,"featured_media":28744,"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\/1801"}],"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=1801"}],"version-history":[{"count":12,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1801\/revisions"}],"predecessor-version":[{"id":44128,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1801\/revisions\/44128"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/28744"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=1801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=1801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=1801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}