Combined Variation

• Combined variation


  A physical relationship involving both direct and inverse variation, as well as joint variation, between variables
• Defining combined variation


  1. Translate into variation statement

  2. Identify a relationship involving combined variation between two quantities

  3. Solve problems involving combined variation
• Direct variation


  y = kx, where y varies directly with x
• Inverse variation


  y = k/x, where y varies inversely with x
• Joint variation


  a = kbc, where a varies jointly as b and c
• Translating combined variation statements


  z = kx/y, where z varies directly as x and inversely as y
• Solving problems with combined variation

  Identify the constant of variation k

  2. Substitute known values into the variation equation

  3. Solve for the unknown variable
• Solving combined variation problems


  • z = 9 when x = 6, y = 2; find z when x = 8, y = 12

  r = 2 when s = 18, u = 2; find r when u = 3, s = 27

  find s when r = 4, u = 2