math help

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! 

Version:1.0 StartHTML:000000282 EndHTML:000010119 StartFragment:000006053 EndFragment:000009993 StartSelection:000006056 EndSelection:000009989 SourceURL:https://edge.apus.edu/portal/site/359685/tool/a222a381-889d-4348-be49-8bec1d56880c/discussionForum/message/dfViewThread                              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”: “MATH110 A006 Fall 17”,                 “shortDescription” : “”,                 “locale”: “en-US”,                 “user”: {                     “id”: “22fa47f1-2062-4ef3-9f7c-19fa31c88abb”,                     “eid”: “4705510”                 },                 “timeoutDialog” : {                 “enabled”: true,                 “seconds”: 600                 },                 “toggle” : {                     “allowauto”: false,                     “tools”: false,                     “sitenav”: false // This is not allowed in morpheus                 },                 “pageScriptPath” : “/library/js/”,                 “portalCDNQuery” : “?version=11.x_A08”             };              
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.

Version:1.0 StartHTML:000000282 EndHTML:000020532 StartFragment:000006053 EndFragment:000020406 StartSelection:000006053 EndSelection:000020377 SourceURL:https://edge.apus.edu/portal/site/359685/tool/a222a381-889d-4348-be49-8bec1d56880c/discussionForum/message/dfViewThread                              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”: “MATH110 A006 Fall 17”,                 “shortDescription” : “”,                 “locale”: “en-US”,                 “user”: {                     “id”: “22fa47f1-2062-4ef3-9f7c-19fa31c88abb”,                     “eid”: “4705510”                 },                 “timeoutDialog” : {                 “enabled”: true,                 “seconds”: 600                 },                 “toggle” : {                     “allowauto”: false,                     “tools”: false,                     “sitenav”: false // This is not allowed in morpheus                 },                 “pageScriptPath” : “/library/js/”,                 “portalCDNQuery” : “?version=11.x_A08”             };              
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:
 
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)
                                                                      8x + 11y  = 1140     (eliminate x- variable)
o $8x + $11y = $1140                                           3y   = 180        (isolate y 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)
                                                                   x   =  60     (simple subtraction to isolate x)
o $8x + $11y = $1140                               x   =  60       (solve)
                                                                                                                                
Checking the answers:
o x + y = 120                             (60) +     (60) =    120   (substitute known variables)
                                                8(60) + 11(60) =    1140 (Solve)
o $8x + $11y = $1140
 
SOLUTION: Rosaria purchased 60 bracelets and 60  necklaces.                  
 what will be the response to this person