{"id":140,"date":"2020-04-18T11:00:22","date_gmt":"2020-04-18T15:00:22","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=140"},"modified":"2021-09-08T14:01:25","modified_gmt":"2021-09-08T18:01:25","slug":"learning-activities-answer-key","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/learning-activities-answer-key\/","title":{"raw":"Chap 1 Knowledge Check Answer Key","rendered":"Chap 1 Knowledge Check Answer Key"},"content":{"raw":"

Knowledge Check 1.1<\/h2>\r\n
    \r\n \t
  1. a. $9,000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $66,000<\/li>\r\n \t
  2. Sounders: [latex]\\frac{$936,400}{$184,000}[\/latex], Elecktronicks: [latex]\\frac{$1,245,900}{$209,400}[\/latex] (Elecktronicks is better)<\/li>\r\n<\/ol>\r\n

    Knowledge Check 1.2<\/h2>\r\n1. a. Net Profit = 14% of [latex]$29,000 = 0.14\\times $29,000 = $ 4,060[\/latex].\r\n\r\nb. [latex]Sales \\times 0.14 =$5,000[\/latex], so [latex]Sales = \\frac{$5,000}{0.14} =$35,714.29[\/latex]\r\n\r\n2 a. $9.80\u00a0 b. $22.40\u00a0 c. $39.20\r\n

    Knowledge Check 1.3<\/h2>\r\n1.a. COGS = 0.65 \u00d7 $ 90,000 =\u00a0\u00a0 $58,500\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Sales<\/td>\r\n$90,000<\/td>\r\n<\/tr>\r\n
    COGS<\/td>\r\n58,500<\/td>\r\n<\/tr>\r\n
    Gross Profit<\/td>\r\n31,500<\/td>\r\n<\/tr>\r\n
    Operating Expenses<\/td>\r\n14,000<\/td>\r\n<\/tr>\r\n
    Net Profit<\/td>\r\n17,500<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. [latex]\\text{Percent gross margin} =\\frac{$31,500}{$90,000} = 0.35 = 35%[\/latex]\r\n\r\n \r\n

    Knowledge Check 1.4<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\nCOST<\/strong><\/td>\r\n% MARKUP<\/strong><\/td>\r\nMARKUP<\/strong><\/td>\r\nPRICE<\/strong><\/td>\r\n<\/tr>\r\n
    a.<\/td>\r\n$10.00<\/td>\r\n35%<\/td>\r\n$3.50<\/td>\r\n$13.50<\/td>\r\n<\/tr>\r\n
    b.<\/td>\r\n$20.00<\/td>\r\n45%<\/td>\r\n$9.00<\/td>\r\n$29.00<\/td>\r\n<\/tr>\r\n
    C.<\/td>\r\n$16.00<\/td>\r\n25%<\/td>\r\n$4.00<\/td>\r\n$20.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n

    Knowledge Check 1.5<\/h2>\r\n1. a.\r\n\r\n[latex]\r\n\r\n\\begin{align*}\r\n\r\n&200 \u20ac &=& 200 \u20ac \\times \\frac{$1.532}{1 \u20ac }&=&$306.40\\\\\r\n\r\n&200 \\text{ HKD} &=& 200 \\text{ HKD} \\times \\frac{$0.1678}{1\\text{ HKD} }&=&$33.56\\\\\r\n\r\n&200\u00a5 &=& 200 \\: \\yen \\times \\frac{$0.011648}{1\u00a5}&=&$2.33\r\n\r\n\\end{align*}[\/latex]\r\n\r\nb.\r\n\r\n[latex]\\begin{align*}\r\n\r\n$500 &=& $500 \\times \\frac{1\u20ac}{$1.532}&=&326.37\u20ac\\\\\r\n\r\n$500 &=& $500 \\times \\frac{1\\;HKD}{$0.1678}&=&2,979.74\\;HKD\\\\\r\n\r\n$500 &=& $500 \\times \\frac{1\\yen}{$0.011648}&=&42,925.82\\yen\r\n\r\n\\end{align*}[\/latex]\r\n

    Knowledge Check 1.6<\/h2>\r\n
      \r\n \t
    1. [latex] 700(1-0.3)(1-0.25) =$ 367.50[\/latex]<\/li>\r\n \t
    2. Discount = [latex] 349-$ 244.30 =$ 104.70[\/latex]<\/li>\r\n<\/ol>\r\n[latex]\\text{Discount Rate} =\\frac{$104.70}{$349}=0.30=30%[\/latex]\r\n\r\n \r\n

      Knowledge Check 1.7<\/h2>\r\nBefore Discount: [latex]6\\times $ 749 (1-0.3)(1-0.05) = $ 2,988.51[\/latex]\r\n\r\nAfter Discount: [latex]2,988.51(1-0.03)=$2,898.85[\/latex]\r\n\r\n \r\n

      Knowledge Check 1.8<\/h2>\r\n
        \r\n \t
      1. The last day you can pay off both debts is the day the fridge invoice is due:\u00a0 May 4.\u00a0 On this day, the fridge will not get a discount, but the range will be eligible for a 5% discount<\/li>\r\n \t
      2. The first payment of $760 is worth a credit of:<\/li>\r\n<\/ol>\r\n

        [latex]Credit = \\frac{$760}{(1-0.05)}=$800[\/latex]<\/p>\r\nso the we owe [latex]$2,500-$800=$1,700[\/latex] on the fridge, and [latex]$3,250(1-0.05)=$ 3,087.50[\/latex] on the range, so our final payment will be:\r\n

        [latex]Payment =$1,700+$3,087.50 = $4,787.50[\/latex]<\/p>","rendered":"

        Knowledge Check 1.1<\/h2>\n
          \n
        1. a. $9,000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $66,000<\/li>\n
        2. Sounders: [latex]\\frac{$936,400}{$184,000}[\/latex], Elecktronicks: [latex]\\frac{$1,245,900}{$209,400}[\/latex] (Elecktronicks is better)<\/li>\n<\/ol>\n

          Knowledge Check 1.2<\/h2>\n

          1. a. Net Profit = 14% of [latex]$29,000 = 0.14\\times $29,000 = $ 4,060[\/latex].<\/p>\n

          b. [latex]Sales \\times 0.14 =$5,000[\/latex], so [latex]Sales = \\frac{$5,000}{0.14} =$35,714.29[\/latex]<\/p>\n

          2 a. $9.80\u00a0 b. $22.40\u00a0 c. $39.20<\/p>\n

          Knowledge Check 1.3<\/h2>\n

          1.a. COGS = 0.65 \u00d7 $ 90,000 =\u00a0\u00a0 $58,500<\/p>\n\n\n\n\n\n\n\n
          Sales<\/td>\n$90,000<\/td>\n<\/tr>\n
          COGS<\/td>\n58,500<\/td>\n<\/tr>\n
          Gross Profit<\/td>\n31,500<\/td>\n<\/tr>\n
          Operating Expenses<\/td>\n14,000<\/td>\n<\/tr>\n
          Net Profit<\/td>\n17,500<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          2. [latex]\\text{Percent gross margin} =\\frac{$31,500}{$90,000} = 0.35 = 35%[\/latex]<\/p>\n

           <\/p>\n

          Knowledge Check 1.4<\/h2>\n\n\n\n\n\n\n
          <\/td>\nCOST<\/strong><\/td>\n% MARKUP<\/strong><\/td>\nMARKUP<\/strong><\/td>\nPRICE<\/strong><\/td>\n<\/tr>\n
          a.<\/td>\n$10.00<\/td>\n35%<\/td>\n$3.50<\/td>\n$13.50<\/td>\n<\/tr>\n
          b.<\/td>\n$20.00<\/td>\n45%<\/td>\n$9.00<\/td>\n$29.00<\/td>\n<\/tr>\n
          C.<\/td>\n$16.00<\/td>\n25%<\/td>\n$4.00<\/td>\n$20.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

           <\/p>\n

          Knowledge Check 1.5<\/h2>\n

          1. a.<\/p>\n

          [latex]\\begin{align*} &200 \u20ac &=& 200 \u20ac \\times \\frac{$1.532}{1 \u20ac }&=&$306.40\\\\ &200 \\text{ HKD} &=& 200 \\text{ HKD} \\times \\frac{$0.1678}{1\\text{ HKD} }&=&$33.56\\\\ &200\u00a5 &=& 200 \\: \\yen \\times \\frac{$0.011648}{1\u00a5}&=&$2.33 \\end{align*}[\/latex]<\/p>\n

          b.<\/p>\n

          [latex]\\begin{align*} $500 &=& $500 \\times \\frac{1\u20ac}{$1.532}&=&326.37\u20ac\\\\ $500 &=& $500 \\times \\frac{1\\;HKD}{$0.1678}&=&2,979.74\\;HKD\\\\ $500 &=& $500 \\times \\frac{1\\yen}{$0.011648}&=&42,925.82\\yen \\end{align*}[\/latex]<\/p>\n

          Knowledge Check 1.6<\/h2>\n
            \n
          1. [latex]700(1-0.3)(1-0.25) =$ 367.50[\/latex]<\/li>\n
          2. Discount = [latex]349-$ 244.30 =$ 104.70[\/latex]<\/li>\n<\/ol>\n

            [latex]\\text{Discount Rate} =\\frac{$104.70}{$349}=0.30=30%[\/latex]<\/p>\n

             <\/p>\n

            Knowledge Check 1.7<\/h2>\n

            Before Discount: [latex]6\\times $ 749 (1-0.3)(1-0.05) = $ 2,988.51[\/latex]<\/p>\n

            After Discount: [latex]2,988.51(1-0.03)=$2,898.85[\/latex]<\/p>\n

             <\/p>\n

            Knowledge Check 1.8<\/h2>\n
              \n
            1. The last day you can pay off both debts is the day the fridge invoice is due:\u00a0 May 4.\u00a0 On this day, the fridge will not get a discount, but the range will be eligible for a 5% discount<\/li>\n
            2. The first payment of $760 is worth a credit of:<\/li>\n<\/ol>\n

              [latex]Credit = \\frac{$760}{(1-0.05)}=$800[\/latex]<\/p>\n

              so the we owe [latex]$2,500-$800=$1,700[\/latex] on the fridge, and [latex]$3,250(1-0.05)=$ 3,087.50[\/latex] on the range, so our final payment will be:<\/p>\n

              [latex]Payment =$1,700+$3,087.50 = $4,787.50[\/latex]<\/p>\n","protected":false},"author":883,"menu_order":12,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-140","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/140\/revisions"}],"predecessor-version":[{"id":3908,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/140\/revisions\/3908"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/140\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=140"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=140"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=140"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}