Question

A fruit company delivers its fruit in two types of boxes large and small a delivery of three large boxes and five box that has a total weight of 71 Kilograms of delivery of six large boxes and two small boxes has a total weight of 92 kilograms how much does each type of weigh

Answer 1

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 $x$.

And let the weight of small box be $y.$

A delivery of three large boxes and five small boxes has a total weight of 71 kilograms:

$3x+5y=71\ \ \ .....(1)$

And, the delivery of six large boxes and two small boxes has a total weight of 92 kilograms:

$6x+2y=92\\\\Subtracting\ both\ sides\ by\ 6x:\\\\2y=92-6x\\\\Dividing\ both\ sides \ by\ 2\ we\ get:\\\\y=46-3x\ \ \ \ ......(2)$

Now, substituting the value of $y$ from equation (2) in equation (1):

$3x+5y=71\\\\3x+5(46-3x)=71$

$3x+230-15x=71\\\\230-12x=71$

Subtracting 230 on both sides we get:

$-12x=-159$

Dividing both sides by -12 we get:

$x=13.25.$

The weight of large box = 13.25 kilograms.

Now, substituting the value of $x$ in equation (1) we get:

$3x+5y=71\\\\3(13.25)+5y=71\\\\39.75+5y=71\\\\Subtracting\ both\ sides by\ 39.75\ we\ get:\\\\5y=31.25\\\\Dividing\ both\ sides\ by\ 5\ we\ get:\\\\y=6.25.$

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.