Respuesta :
Answer:
The weight of large box is 13.25 kilograms and the weight of small box is 6.25 kilograms.
Step-by-step explanation:
Given:
A fruit company delivers its fruit in two types of boxes large and small a delivery of three large boxes and five small boxes that has a total weight of 71 kilograms and a delivery of six large boxes and two small boxes has a total weight of 92 kilograms.
Now, to find the weight of each type of box.
Let the weight of large box be [tex]x[/tex].
And let the weight of small box be [tex]y.[/tex]
A delivery of three large boxes and five small boxes has a total weight of 71 kilograms:
[tex]3x+5y=71\ \ \ .....(1)[/tex]
And, the delivery of six large boxes and two small boxes has a total weight of 92 kilograms:
[tex]6x+2y=92\\\\Subtracting\ both\ sides\ by\ 6x:\\\\2y=92-6x\\\\Dividing\ both\ sides \ by\ 2\ we\ get:\\\\y=46-3x\ \ \ \ ......(2)[/tex]
Now, substituting the value of [tex]y[/tex] from equation (2) in equation (1):
[tex]3x+5y=71\\\\3x+5(46-3x)=71\\\\[/tex]
[tex]3x+230-15x=71\\\\230-12x=71\\\\[/tex]
Subtracting 230 on both sides we get:
[tex]-12x=-159[/tex]
Dividing both sides by -12 we get:
[tex]x=13.25.[/tex]
The weight of large box = 13.25 kilograms.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]3x+5y=71\\\\3(13.25)+5y=71\\\\39.75+5y=71\\\\Subtracting\ both\ sides by\ 39.75\ we\ get:\\\\5y=31.25\\\\Dividing\ both\ sides\ by\ 5\ we\ get:\\\\y=6.25.[/tex]
The weight of small box = 6.25 kilograms.
Therefore, the weight of large box is 13.25 kilograms and the weight of small box is 6.25 kilograms.
