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A fruit company delivers it’s fruit and two types of boxes large and small delivery of five large boxes and six more boxes has a total weight of 175 kg a delivery of three large boxes and two small boxes has a total weight of 83 kg how much does each type of box weigh ?

 Apr 6, 2020
 #2
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Let a be the weight of Large box

and Let b be the weight of Small box

 

therefore, the equation will be

   =>  5a + 6b = 175kg ----------(1)

         3a + 2b = 83kg ------(2)

  now, Multiplying  equation (2) by 3 on both sides

we get,

       3a*3  + 2b*3 = 83*3

   =>  9a + 6b = 249 -----(3)

 

now subtracting equ. 2 and equ. 3

we get,

        

        5a + 6b = 175

  (-) 9a(-)+6b =(-)249

-------------------------   

    =>  -4a = -74

                 a =  -74/-4 

 

               --------------

              /   a=  18.5   /

                -------------

Therefore the weight of the large box is 18.5 kg

now ,

subtituting value of a in equation b

we get,

       3a + 2b = 83

=> 3*(18.5) + 2b = 83

        55.5 + 2b = 83

          2b = 83 - 55.5

          2b = 27.5

            b = 27.5 / 2

        -----------------

       /   b = 13.75    /

        -----------------

              Therefore the weight of the small box is 13.75kg

and the weight of large box is 18.5kg 

 Apr 6, 2020

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