maths problem

Question

pls help!

 

question-

 

three fruits: an orange, a banana and a cherry are weighed, two at a time. the orange and the banana weigh 130 g, the banana and the cherry weigh 110 g, and the orange and the cherry weigh 80 g. can you find the weight of all the three fruits together? Now try to find the weight of each fruit.

Answer 1

Let's use mnemonic variables (but use R for orange to avoid confusion with 0).

  Let:

   R = weight of an orange

   B = weight of a banana

   C = weight of a cherry

 

Translate:

  "the orange and the banana weigh 130 g"     means    R + B = 130     (eq1)

  "the banana and the cherry weigh 110 g"     means     B + C = 110     (eq2)

  "the orange and the cherry weigh 80 g"     means   R + C = 80    (eq3)

 

"can you find the weight of all the three fruits together?"

  Simply add the equations together and find (R+B+C):

      R  +  B        =  130

              B +  C =  110

      R       +    C =    80

---------------------------

    2R + 2B + 2C = 320

    2(R+B+C) = 320           (distributive property)

      R+B+C = 160 g

 

"Now try to find the weight of each fruit"

  Simply subtract the appropriate equation to eliminate the other variables:

    To find R:

        R + B + C = 160

              B + C = 110    (eq2)

      ---------------------

        R             = 50g

 

    To find B:

        R + B + C = 160

        R       + C =  80    (eq3)

   ------------------------

              B       = 80g

 

   To find C:

       R + B + C = 160

       R + B       =  130    (eq1)

   ------------------------

                    C =  30g

 

Checking is important:

  Is  (eq1)    R+B = 130  ?

                  50+80 = 130  ?

                     130 = 130  ?yes

  Is (eq2)   B+C=110  ?

                 80+30 = 110  ?

                   110 = 110  ?yes

  Is (eq3)  R+C = 80  ?

                  50+30 = 80  ?

                     80 = 80  ?yes

                      

 

Answer 2

Let R represent the weight of the orange, B the weight of the banana, and C the weight of the cherry.  Then create the system with equations 1R+1B+0C=130, 0R+1B+1C=110, and 1R+0B+1C=80.  There are many paths to the only solution of this system.  One is to work with the matrix with row #1 = 1  1  0  130,  row #2 = 0  1  1  110 and Row #3 = 1  0  1  80.  If -1 times row #1 is added to row #3 the third row is changed, but the solution of the system is not.  The new Row #3 is 0  1  -1  -50.  Then if row #2 is added to this new row #3, we get a new row #3, but again the solution of the system is not changed.  The new row #3 is 0  0  2  60.  From this we can see that the weight of a cherry is 30 grams, the weight of a banana (from row #2) is 80 grams, and the weight of an orange is 50 grams (from row #1).  Therefore the weight of the three pieces of fruit together is 160 grams and the individual weights.  The individual weights are already known.