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A fruit company delivers its fruit in two types of boxes : large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 190 kilograms. A delivery of 2 large boxes and 3 small boxes has a total of 84 kilograms. How much does each type of boxes weigh ?

Respuesta :

TeamAlsina
4 large and 8 small weigh 113kg 
so 
2 large and 4 small weigh 56.5 kg 
but 
2 large and 3 small weigh 50 kg 
so taking the difference 
1 small weighs 56.5 - 50 = 6.5 kg. 

Substitute : 
2 large and 3 small weight 50 kg 
2 large weigh 50 - 3*6.5 = 50 - 19.5 = 30.5 kg 
1 large weighs 15.25 kg
axv7975

We  have  this  system

6L  +  5S   =  190       (1)

2L  +  3S   =   84     multiply  through  by -3  ⇒ -6L  - 9S   = -252   (2)

Add  (1)  and (2)    and  we  get  that

-4S   =  -62

S = -62  / -4     =   15.5  kilos  for  a small box  

And

2L  +  3S  =  84

2L  + 3 (15.5)  =  84

2L  =  46.5   =  84

2L  =  84  - 46.5

2L  = 37.5

L = 37.5 /2    =  18.75  kilos  for a large box

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