Question
For Problem #s 1 and 2, show a valid system of equations/inequalities that could be used to solve each problem. You will only receive credit for the system; you will not receive credit for the solution.
1. At the end of a day, a toll collector counts the number of nickels and quarters deposited at the exact change lane. There is a total of 54572 coins and a total of $12944.40 collected. Write a system of linear equations to model this situation.

2. Alex is packing books into boxes. Each box holds either 12 small books or 7 larger books. Alex cannot use more than 30 boxes; however, he must pack a minimum of 250 books. Write a system of linear inequalities to model this situation.

For Problem #s 3 and 4, solve by using any method demonstrated in class. Please show the system of equations you used, all work, and correct units. If using a TI83/84, show the window settings ( Xmin , Xmax ) and ( Ymin , Ymax ) and coordinates of the intersection point.
3. A person invests a total of $25000 in the stock market. Some of this was invested in precious metals commodities, which earned 9.5% simple interest per year, and the rest was invested in crude oil commodities, which earned 7.25% simple interest per year. If the total interest earned after one year is $2001.50, how much money was invested in each commodity?

4. A jeweler needs to mix two copper alloys. One alloy contains 17% copper, and a second alloy contains 54% copper. How many ounces of each alloy must be mixed to obtain 48 ounces of another alloy that is 29% copper? (Please round all answers to the nearest hundredth.)
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      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheMissed (276μs)
      • Illuminate\Database\Events\StatementPrepared (723μs)
      • Illuminate\Database\Events\QueryExecuted (841μs)
      • eloquent.retrieved: App\Models\SubjectCat (58μs)
      • Illuminate\Cache\Events\KeyWritten (305μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • creating: site.layouts.app (353μs)
      • composing: site.layouts.app (16μs)
      • creating: components.canonical (373μs)
      • composing: components.canonical (76μs)
      • creating: components.open-graph (136μs)
      • composing: components.open-graph (46μs)
      • creating: site.headers.header (309μs)
      • composing: site.headers.header (57μs)
      • Illuminate\Cache\Events\CacheHit (1.22ms)
      • creating: components.footer (61μs)
      • composing: components.footer (62μs)
      • Illuminate\Cache\Events\CacheHit (580μs)
      • Illuminate\Cache\Events\CacheMissed (242μs)
      • Illuminate\Database\Events\StatementPrepared (645μs)
      • Illuminate\Database\Events\QueryExecuted (805μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (271μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • creating: components.forms.contact-us (179μs)
      • composing: components.forms.contact-us (97μs)
      • creating: components.forms.get-started (114μs)
      • composing: components.forms.get-started (45μs)
      • creating: components.forms.free-tool-download (82μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (101μs)
      • composing: components.forms.claim-free-worksheet (41μs)
      • creating: components.forms.tutor-subscription-waitlist (79μs)
      • composing: components.forms.tutor-subscription-waitlist (37μs)
      • creating: components.forms.tutor-subscription-join (76μs)
      • composing: components.forms.tutor-subscription-join (37μs)
      • creating: components.forms.tutor-support (73μs)
      • composing: components.forms.tutor-support (39μs)
      • 311 x Illuminate\Cache\Events\CacheHit (13.75%)
        53.38ms
        20 x Illuminate\Database\Events\StatementPrepared (9.73%)
        37.76ms
        20 x Illuminate\Database\Events\QueryExecuted (7.01%)
        27.20ms
        11 x Illuminate\Cache\Events\CacheMissed (1.93%)
        7.48ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.99%)
        3.85ms
        11 x Illuminate\Cache\Events\KeyWritten (0.88%)
        3.40ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.28%)
        1.07ms
        1 x Illuminate\Routing\Events\Routing (0.24%)
        928μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.22%)
        839μs
        1 x creating: components.canonical (0.1%)
        373μs
        1 x Illuminate\Routing\Events\RouteMatched (0.09%)
        357μs
        1 x creating: site.layouts.app (0.09%)
        353μs
        1 x creating: site.headers.header (0.08%)
        309μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        282μs
        1 x creating: components.breadcrumbs (0.07%)
        276μs
        1 x creating: homework.show (0.06%)
        248μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        241μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        228μs
        1 x creating: components.forms.contact-us (0.05%)
        179μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        175μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        169μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        163μs
        1 x creating: components.open-graph (0.04%)
        136μs
        1 x composing: components.breadcrumbs (0.03%)
        118μs
        1 x composing: homework.show (0.03%)
        114μs
        1 x creating: components.forms.get-started (0.03%)
        114μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        101μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        100μs
        1 x composing: components.forms.contact-us (0.02%)
        97μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        94μs
        1 x creating: components.forms.free-tool-download (0.02%)
        82μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        79μs
        1 x composing: components.canonical (0.02%)
        76μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        76μs
        1 x creating: components.forms.tutor-support (0.02%)
        73μs
        1 x composing: components.footer (0.02%)
        62μs
        1 x creating: components.footer (0.02%)
        61μs
        1 x composing: site.headers.header (0.01%)
        57μs
        1 x composing: components.open-graph (0.01%)
        46μs
        1 x composing: components.forms.get-started (0.01%)
        45μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        43μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        41μs
        1 x composing: components.forms.free-tool-download (0.01%)
        40μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        39μs
        1 x composing: components.forms.tutor-support (0.01%)
        39μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        38μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        37μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        37μs
        1 x composing: site.layouts.app (0%)
        16μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated52.58ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '13585' limit 1
        23.18mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 13585
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (9)
        890μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (13585)
        860μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        920μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 13585 and `subject` = 9 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        9.39mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 13585
        • 1: 9
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (9)
        1.36mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 13585 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.21mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 13585
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 13585 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        3.32mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 13585
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 13585 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        800μstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        990μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        960μstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        860μstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        990μstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        960μstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        900μstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        940μstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        940μstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
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          utm_source
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          PHPDEBUGBAR_STACK_DATA
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          status_text
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          request_query
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          request_request
          []
          
          request_headers
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          request_cookies
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