word problem question

Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2

 large boxes and 3

 small boxes has a total weight of 57

 kilograms. A delivery of 6

 large boxes and 5

 small boxes has a total weight of 145

 kilograms. How much does each type of box weigh? 

weight of each large box:

weight of each small box:

in kilograms

Answer 1

Hi Lujain

Small box weighs 6.5 kgs

Large box weight 18.75 kegs

You can use a system of equations to solve your problem with elimination or substitution

Let l = large box

Let s = small box

According to the information given

2l + 3s = 57

6l + 5s = 145

If you multiply the first equation by -3 you can eliminate l when you combine it with the second equation

-3(2l + 3s = 57) becomes

-6l - 9s = -171

Now combine this with the second equation

-6l - 9s = -171

6l + 5s = 145

We have

-4s = -26

s = 6.5

Use this value in the original equation to solve for l

2l + 3(6.5) = 57

2l + 19.5 = 57

2l = 57 - 19.5

2l = 37.5

l = 18.75

Checking in the second equation

6(18.75) + 5(6.5) = 145

112.5 + 32.5 = 145

I hope this helps.

Answer 2

2L + 3S = 57

6L + 5S = 145

Suggestion: multiplhy top equation by 3 and then subtract the bottom equation from it.

Solve for S