procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I’m sure that a “thank you” for an exceptionally clear explanation would also be welcome!Version:1.0 StartHTML:000000283 EndHTML:000006287 StartFragment:000005843 EndFragment:000006149 StartSelection:000005843 EndSelection:000006149 SourceURL:https://edge.apus.edu/portal/site/359685/tool/a222a381-889d-4348-be49-8bec1d56880c/discussionForum/message/dfAllMessages var sakai = sakai || {}; sakai.editor = sakai.editor || {}; sakai.editor.editors = sakai.editor.editors || {}; sakai.editor.editors.ckeditor = sakai.editor.editors.ckeditor || {}; sakai.locale = sakai.locale || {}; sakai.locale.userCountry = ‘US’; sakai.locale.userLanguage = ‘en’; sakai.locale.userLocale = ‘en_US’; sakai.editor.collectionId = ‘/group/359685/’; sakai.editor.enableResourceSearch = false; sakai.editor.siteToolSkin = ‘/library/skin/apus/tool.css’; sakai.editor.sitePrintSkin = ‘/library/skin/apus/print.css’; sakai.editor.editors.ckeditor.browser = ‘elfinder’; var CKEDITOR_BASEPATH=’/library/webjars/ckeditor/4.5.7/full/’; .cke{visibility:hidden;} APUS CLE : MATH110 A006 Fall 17 : Forums var portal = { “chat”: { “enabled”: false, “pollInterval”: 5000, “video” : { “enabled”: true } }, “loggedIn”: true, “portalPath”: “https://edge.apus.edu/portal”, “loggedOutUrl”: “https://edge.apus.edu/portal”, “siteId”: “359685”, “siteTitle”: “/library/js/”, “portalCDNQuery” : “?version=11.x_A08” };
You must also respond to 2 classmates. A request for clarification on the procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I’m sure that a “thank you” for an exceptionally clear explanation would also be welcome!
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A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there?
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Let x equal the number of $5 bills
Let y equal the number of $20 bills
We know that together the number of $5 bills and the $20 bills is 54, so that is the first equation.
x + y = 54
Next the total value of the bills combined is $780, that is the second equation.
5x + 20y = 780
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Now that we have our two equations we can solve by substitution. To do so we have to rearrange our first equation solving for one of the variables
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x + y = 54
– x        – x
y = 54 – x
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Next we will substitute this equation into the second, and solve.
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5x + 20(54 – x) = 780Â Â Â Â Â Â Â (multiply 20 and 54, and multiply 20 and – x)
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5x + 1080 – 20x = 780      (combine 5x and – 20x)
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-15x + 1080 = 780Â Â Â Â Â Â Â Â (subtract 1080 from both sides)
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-15x = -300Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (divide by -15)
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x = 20
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Now that we have our x value, we can solve for y using our first equation.
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20 + y = 54Â Â Â (subtract 20 from each side)
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y = 34
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Finally, to check the answers you substitute them into both of the equations.
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20 + 34 = 54
       54 = 54  TRUE
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5(20) + 20(34) = 780
      100 + 680 = 780
                780 = 780 TRUE
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The final answer is there are 20 – $5 bills, and 34 – $20 bills.
what will be a response to this person.
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The Problem: (x) number of bracelets are sold at $8 each and (y) number of necklaces at $11 each. Rosaria paid a total of $1140. How many bracelets and how many necklaces did she purchase?
The Solution:
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1.) Â Listed are the known factors:
o Let the number of bracelets be represented by the variable:Â Â Â x
In which each x number of bracelets are priced at $8
o Let the number of necklaces be represented by the variable: Â Â y
In which each y number of necklaces are priced at $11
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2.) Â Listed are the relationships between x and y
o x + y = 120
o $8x + $11y = $1140
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3.) Â I will be using both elimination and substitution process to solve this problem
.
First I’d use the elimination process to solve the system of equations: Â
o -8[x + y = 120]                                         -8x – 8y   = -(960)   (multiply equation by -8)
                                                                     8x + 11y = 1140    (eliminate x- variable)
o $8x + $11y = $1140                                          3y  = 180        (isolate y through division)
                                                                                                     3          3
                                                                                             y   = 60            (solve)
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Second I’d use the substitution process to solve for the x-variable:
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o x + y = 120Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â x + (60) = Â 120Â Â Â (substitute known variable: y)
                                                                  x  =  60    (simple subtraction to isolate x)
o $8x + $11y = $1140                               x   =  60      (solve)
                                                                                                                               Â
Checking the answers:
o x + y = 120Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (60) + Â Â Â Â (60) = Â Â Â 120 Â Â (substitute known variables)
                                                8(60) + 11(60) =    1140 (Solve)
o $8x + $11y = $1140
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SOLUTION: Rosaria purchased 60 bracelets and 60 necklaces.                 Â
what will be the response to this person