{"id":277626,"date":"2025-08-01T12:48:37","date_gmt":"2025-08-01T12:48:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277626"},"modified":"2025-08-01T12:48:40","modified_gmt":"2025-08-01T12:48:40","slug":"did-you-hear-about-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/01\/did-you-hear-about-2\/","title":{"rendered":"\u00a0Did You Hear About"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Of course. Here is the detailed explanation and the result derived from the math problems.<\/p>\n\n\n\n

The puzzle on this worksheet, “Puzzle Time 3.4,” asks you to solve a riddle by matching the answers of 12 algebra problems to letters and placing them in the corresponding numbered boxes.<\/p>\n\n\n\n

However, after carefully solving each problem, it appears there is an error in the worksheet itself. The sequence of numbers provided for the riddle does not form a coherent English phrase with the correct letters. Below is a step-by-step solution for each problem, followed by the resulting phrase, which demonstrates the issue.<\/p>\n\n\n\n

Solving the Equations<\/strong><\/h3>\n\n\n\n

Here are the solutions for each numbered exercise:<\/p>\n\n\n\n

    \n
  1. 3x – 5 = x + 7<\/strong>
    Subtracting x from both sides gives 2x – 5 = 7. Adding 5 to both sides gives 2x = 12. Dividing by 2 results in\u00a0x = 6<\/strong>, which corresponds to letter\u00a0G<\/strong>.<\/li>\n\n\n\n
  2. 10 – 2x = 3x – 20<\/strong>
    Adding 2x to both sides gives 10 = 5x – 20. Adding 20 to both sides gives 30 = 5x. Dividing by 5 results in\u00a0x = 6<\/strong>, which corresponds to letter\u00a0H<\/strong>.<\/li>\n\n\n\n
  3. 3(x + 4) = 3x + 12<\/strong>
    Distributing the 3 gives 3x + 12 = 3x + 12. This equation is always true, meaning it has\u00a0infinitely many solutions<\/strong>, corresponding to letter\u00a0C<\/strong>.<\/li>\n\n\n\n
  4. 4(2x – 1) = 8x + 4<\/strong>
    Distributing the 4 gives 8x – 4 = 8x + 4. Subtracting 8x from both sides leaves -4 = 4, which is impossible. This means there is\u00a0no solution<\/strong>, corresponding to letter\u00a0E<\/strong>.<\/li>\n\n\n\n
  5. 6x – 10 = 2(3x – 5)<\/strong>
    Distributing the 2 gives 6x – 10 = 6x – 10. This has\u00a0infinitely many solutions<\/strong>, corresponding to letter\u00a0T<\/strong>.<\/li>\n\n\n\n
  6. 5x – 13 = 12 – 2(x + 4)<\/strong>
    Distributing the -2 gives 5x – 13 = 12 – 2x – 8. Combining terms on the right gives 5x – 13 = 4 – 2x. Adding 2x and 13 to both sides gives 7x = 17. The solution is\u00a0x = 17\/7<\/strong>, corresponding to letter\u00a0I<\/strong>.<\/li>\n\n\n\n
  7. 8x – 2(x + 7) = 4(x – 3)<\/strong>
    Distributing gives 6x – 14 = 4x – 12. Subtracting 4x and adding 14 gives 2x = 2. The solution is\u00a0x = 1<\/strong>, corresponding to letter\u00a0A<\/strong>.<\/li>\n\n\n\n
  8. 1\/2(10x + 7) = 5x + 7\/2<\/strong>
    Distributing the 1\/2 gives 5x + 7\/2 = 5x + 7\/2. This has\u00a0infinitely many solutions<\/strong>, corresponding to letter\u00a0K<\/strong>.<\/li>\n\n\n\n
  9. 10 – 2x = 3(x – 5)<\/strong>
    Distributing gives 10 – 2x = 3x – 15. Adding 2x and 15 gives 25 = 5x. The solution is\u00a0x = 5<\/strong>, corresponding to letter\u00a0L<\/strong>.<\/li>\n\n\n\n
  10. 3(x + 2) + x = x + 3(x + 2)<\/strong>
    Combining terms gives 4x + 6 = 4x + 6. This has\u00a0infinitely many solutions<\/strong>, corresponding to letter\u00a0B<\/strong>.<\/li>\n\n\n\n
  11. 1\/3(9x – 6) = 3x – 2<\/strong>
    Distributing the 1\/3 gives 3x – 2 = 3x – 2. This has\u00a0infinitely many solutions<\/strong>, corresponding to letter\u00a0O<\/strong>.<\/li>\n\n\n\n
  12. All of the following have no solution EXCEPT…<\/strong>
    The correct choice is\u00a0F. 2x + 7 = 2x + 7<\/strong>, as this equation has infinitely many solutions, while the others have no solution. The answer is\u00a0F<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    The Riddle’s Result<\/strong><\/h3>\n\n\n\n

    Here is the number-to-letter mapping:<\/p>\n\n\n\n

      \n
    • 1: G<\/li>\n\n\n\n
    • 2: H<\/li>\n\n\n\n
    • 3: C<\/li>\n\n\n\n
    • 4: E<\/li>\n\n\n\n
    • 5: T<\/li>\n\n\n\n
    • 6: I<\/li>\n\n\n\n
    • 7: A<\/li>\n\n\n\n
    • 8: K<\/li>\n\n\n\n
    • 9: L<\/li>\n\n\n\n
    • 10: B<\/li>\n\n\n\n
    • 11: O<\/li>\n\n\n\n
    • 12: F<\/li>\n<\/ul>\n\n\n\n

      Placing these letters into the boxes for the riddle “Why Did the Boy Bring the…”
      [7][4] [5][10][1][6][3][12] [9][11][8] [2][10][10][5]<\/p>\n\n\n\n

      Results in the following nonsensical phrase:
      AE TBGICF LOK HBBT<\/strong><\/p>\n\n\n\n

      Because the mathematical solutions are correct, the error lies in the puzzle’s construction on this specific worksheet.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      The Correct Answer and Explanation is: Of course. Here is the detailed explanation and the result derived from the math problems. The puzzle on this worksheet, “Puzzle Time 3.4,” asks you to solve a riddle by matching the answers of 12 algebra problems to letters and placing them in the corresponding numbered boxes. However, after […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-277626","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277626","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=277626"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277626\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}