Afruit company delivers its fruit in two types of boxes: large and small. a delivery of 3 large boxes and 2 small boxes has a total weight of 59 kilograms. a delivery of 8 large boxes and 4 small boxes has a total weight of 149 kilograms. how much does each type of box weigh?

answer:

let l be the weight of a large box and s be the weight of a small box. so we can set up two equations:

2l + 3s = 83

4l + 8s = 197

solve for l or s in one of the equations and substitute it into the other equation and find the other unknown.

2l = 83 - 3s

l = (83 - 3s)/2

4(83 - 3s)/2 + 8s = 197

166 - 6s + 8s = 197

2s = 31

s = 15.5 kg

l = (83 - 3(15.5))/2 = 18.25 kg

plug them in to the original equations to see if they work.

upvote

•

0

downvote

add comment

jesse s. answered • 11/19/17

patient and knowledgeable math tutor

weight of large box = x kg

weight of small box =y kg

2 large boxes and 3 small boxes has a total weight of 83 kilograms.

2x+3y= eq 1

4 large boxes and 8 small boxes has a total weight of 197 kilograms.

4x+8y =197 2

multiply eq 1 with -2

-4x-6y =-166

now add both equations

-4x-6y=-166

4x+8y=197

2y= 31

y=15.5

substitute value of y=17 in eq 1

2x+3y=83

2x+3(15.5)=83

2x+46.5=83

2x =36.5

x=18.25

weight of large box = x kg=18.25kg

weight of small box =y kg=15.5kg

upvote

•

0

downvote

add comment

andy c. answered • 11/19/17

math/physics tutor

2l + 3s = 83

4l + 8s = 197

multiplies the top equation by -2.

-4l + -6s = -166

4l + 8s = 197

adding them

2s = 31

s = 31/2 = 15.5

plugging into the first equation:

2l + 3s = 83

2l + 3(15.5) = 83

2l + 46.5 = 83

2l = 83 - 46.5

2l = 36.5

l = 36.5/2 = 18.25

check:

2l + 3s = 2(18.25) + 3(15.5) = 36.5 + 46.5 = 83

4l + 8s = 4(18.25) + 8(15.5) = 73 + 124 = 197

the large box weighs 18.25

the small box weighs 15.5

step-by-step explanation:

hope this .