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Anna, Bob and Chris did will not disclose their weights but agree to be weighed in pairs. Anna and Bob together weigh 226 pounds. Bob and Christ together weigh 210 pounds. Anna and Chris together weigh 200 pounds. How
does each student weigh?

Respuesta :

varshamittal029

Anna , Bob , Chris weigh 108 pounds , 118 pounds  , 92 pounds respectively .

  • Solve a linear equation in three variables by completing the following steps:
  • Take any two equations and solve them for one variable
  • Again, take two more pairs of equations and solve for the same variables.
  • We have two systems of equations with two unknown variables. solve two equations
  • Again, substitute the calculated values ​​of the variables into one of the original equations and solve for the unknown variables.

Let the Anna weigh = x pounds

Let the Bob weigh = y pounds

Let the Chris weigh = z pounds

According to the question Anna and Bob together weigh 226 pounds which can be written as  [tex]x+y=226[/tex]     ..(1)

According to the question Bob and Christ together weigh 210 pounds. which can be written as   [tex]y+z=210[/tex]      ...(2)

According to the question Anna and Chris together weigh 200 pounds. which can be written as  [tex]x+z=200[/tex]      ..(3)

From equation (1) [tex]y=226-x[/tex]  putting this value in equation (2) , we get

      [tex]226-x+z=210\\16=x-z\\16+z=x[/tex]       ..(4)

Putting above value in equation (3) , we get

     [tex]16+z+z=200\\2z=184\\z=92[/tex]

Putting z = 92 in equation (4) , we get

    [tex]x=16+92\\x=108[/tex]

Putting x = 108 in equation (1) , we get

   [tex]y=226-108\\y=118[/tex]

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