A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 160 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 74 kilograms. How much does each type of box weigh?

Small Box = 13.75 kg

Large Box = 15.5 kg

Step-by-step explanation:

x=wt of small box     y = large box

First delivery

   6x  + 5y = 160      solve for y = 32 - (6/5x)

Second Delivery

  3y + 2x = 74       Substitute for y

  3(32 - (6/5x)) + 2x = 74       and solve for x

   96 - (18/5x) +2x = 74

     x = 13.75

x = 13.75 = small box kg               y = 32 - (6/5x) = large box = 15.5 kg

s

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240