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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”             };              

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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?

 

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

 

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

 

x + y = 54

– x         – x

y = 54 – x

 

Next we will substitute this equation into the second, and solve.

 

5x + 20(54 – x) = 780        (multiply 20 and 54, and multiply 20 and – x)

 

5x + 1080 – 20x = 780      (combine 5x and – 20x)

 

-15x + 1080 = 780         (subtract 1080 from both sides)

  

-15x = -300                (divide by -15) 

 

x = 20 

 

 

Now that we have our x value, we can solve for y using our first equation.

 

20 + y = 54    (subtract 20 from each side)

 

y = 34

 

Finally, to check the answers you substitute them into both of the equations.

 

20 + 34 = 54

        54 = 54   TRUE

 

5(20) + 20(34) = 780

       100 + 680 = 780

                 780 = 780 TRUE

 

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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(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?

 

1.)  Listed are the known factors:

o Let the number of bracelets be represented by the variable:    x

  • In which each x number of bracelets are priced at $8

o Let the number of necklaces be represented by the variable:   y

  • In which each y number of necklaces are priced at $11

 

2.)  Listed are the relationships between x and y 

o x + y = 120

o $8x + $11y = $1140

 

3.)  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:  

o -8[x + y = 120]                                          -8x – 8y    = -(960)    (multiply equation by -8)

                                                                       (eliminate – variable)

o $8x + $11y = $1140                                                  (isolate through division)

                                                                                                      3          3

                                                                                             y   = 60             (solve)

 

 

  • Second I’d use the substitution process to solve for the x-variable:

 

o x + y = 120                                    x + (60) =  120    (substitute known variable: y)

                                                           (simple subtraction to isolate x)

o $8x + $11y = $1140                               x   =  60       (solve)

                                                                                                                                

o x + y = 120                             (60) +     (60) =    120   (substitute known variables)

                                                8(60) + 11(60) =    1140 (Solve)

o $8x + $11y = $1140

 

             

 what will be the response to this person

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