{"id":34015,"date":"2025-06-23T12:44:08","date_gmt":"2025-06-23T12:44:08","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=34015"},"modified":"2025-06-23T12:45:06","modified_gmt":"2025-06-23T12:45:06","slug":"q-as-a-function-of-p-p-as-a-function-of-q","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/q-as-a-function-of-p-p-as-a-function-of-q\/","title":{"rendered":"Q as a function of P P as a function of Q"},"content":{"rendered":"\n

Q as a function of P P as a function of Q Q = 10 – P Q = 25 _ SP 6Q = 30 _<\/p>\n\n\n\n

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

Let’s analyze the given relationships and solve step by step.<\/p>\n\n\n\n

\n\n\n\n

Given:<\/strong><\/h3>\n\n\n\n
    \n
  1. Q=10\u2212PQ = 10 – PQ=10\u2212P<\/li>\n\n\n\n
  2. Q=25\u2212SPQ = 25 – SPQ=25\u2212SP<\/li>\n\n\n\n
  3. 6Q=30\u2212P6Q = 30 – P6Q=30\u2212P<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Step 1: Express each equation in terms of P<\/strong><\/h3>\n\n\n\n

    1. Q=10\u2212PQ = 10 – PQ=10\u2212P<\/h4>\n\n\n\n

    To express PPP as a function of QQQ: P=10\u2212QP = 10 – QP=10\u2212Q<\/p>\n\n\n\n

    2. Q=25\u2212SPQ = 25 – SPQ=25\u2212SP<\/h4>\n\n\n\n

    To find PPP as a function of QQQ, rearrange: SP=25\u2212Q\u21d2P=25\u2212QSSP = 25 – Q \\quad \\Rightarrow \\quad P = \\frac{25 – Q}{S}SP=25\u2212Q\u21d2P=S25\u2212Q\u200b<\/p>\n\n\n\n

    Assuming SSS is a constant (you did not specify its value), this is the general form.<\/p>\n\n\n\n

    3. 6Q=30\u2212P6Q = 30 – P6Q=30\u2212P<\/h4>\n\n\n\n

    Solve for PPP: P=30\u22126QP = 30 – 6QP=30\u22126Q<\/p>\n\n\n\n

    Now solve for QQQ as a function of PPP: 6Q=30\u2212P\u21d2Q=30\u2212P66Q = 30 – P \\quad \\Rightarrow \\quad Q = \\frac{30 – P}{6}6Q=30\u2212P\u21d2Q=630\u2212P\u200b<\/p>\n\n\n\n

    \n\n\n\n

    Correct Answers:<\/strong><\/h3>\n\n\n\n
      \n
    • From equation 1<\/strong>:\n
        \n
      • Q=10\u2212PQ = 10 – PQ=10\u2212P<\/li>\n\n\n\n
      • P=10\u2212QP = 10 – QP=10\u2212Q<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • From equation 2<\/strong>:\n
          \n
        • Q=25\u2212SPQ = 25 – SPQ=25\u2212SP<\/li>\n\n\n\n
        • P=25\u2212QSP = \\frac{25 – Q}{S}P=S25\u2212Q\u200b (as long as S\u22600S \\neq 0S\ue020=0)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • From equation 3<\/strong>:\n
            \n
          • 6Q=30\u2212P6Q = 30 – P6Q=30\u2212P<\/li>\n\n\n\n
          • Q=30\u2212P6Q = \\frac{30 – P}{6}Q=630\u2212P\u200b<\/li>\n\n\n\n
          • P=30\u22126QP = 30 – 6QP=30\u22126Q<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            Explanation <\/strong><\/h3>\n\n\n\n

            In mathematics, expressing one variable as a function of another is a fundamental concept in algebra. Each of the three equations provided describes a linear relationship between quantity QQQ and price PPP.<\/p>\n\n\n\n

            Starting with the first equation Q=10\u2212PQ = 10 – PQ=10\u2212P, this is a linear demand function where quantity decreases as price increases. Rearranging gives P=10\u2212QP = 10 – QP=10\u2212Q, which reflects the inverse relationship \u2014 price as a function of quantity. This is useful for understanding how much price must adjust to meet a desired quantity level.<\/p>\n\n\n\n

            In the second equation Q=25\u2212SPQ = 25 – SPQ=25\u2212SP, a similar structure is presented, but here, the slope SSS is a coefficient on PPP, likely representing sensitivity or elasticity. Solving for PPP gives P=25\u2212QSP = \\frac{25 – Q}{S}P=S25\u2212Q\u200b. This form is often used in economics to analyze how price changes with quantity when the responsiveness of demand (or supply) is influenced by a specific factor SSS.<\/p>\n\n\n\n

            The third equation 6Q=30\u2212P6Q = 30 – P6Q=30\u2212P introduces a multiplier on QQQ. Rearranging it yields two equivalent forms: Q=30\u2212P6Q = \\frac{30 – P}{6}Q=630\u2212P\u200b and P=30\u22126QP = 30 – 6QP=30\u22126Q. Both describe the same relationship. These transformations are essential in algebraic modeling, where solving for different variables allows analysts to make predictions, optimize outcomes, or graph the functions.<\/p>\n\n\n\n

            In summary, expressing variables as functions of one another helps in understanding how changes in one affect the other. These transformations allow the use of equations in multiple contexts \u2014 for example, in economics, business, or optimization problems<\/p>\n\n\n\n

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

            Q as a function of P P as a function of Q Q = 10 – P Q = 25 _ SP 6Q = 30 _ The Correct Answer and Explanation is: Let’s analyze the given relationships and solve step by step. Given: Step 1: Express each equation in terms of P 1. Q=10\u2212PQ = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-34015","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=34015"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34015\/revisions"}],"predecessor-version":[{"id":34017,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34015\/revisions\/34017"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}