Question

Solving a word problem using a system of linear equations of the form Ax + By = C .

Answer 1

x- large box

y small box

5x+3y=87 /×(-4)

2x+12y=105

-20x-12y=-348

2x+12y=105

-18x=-243 /÷(-18)

x=13,5

2×13,5+12y=105

12y=105-27

12y=78 /÷12

y=6,5

large box=13.5kg

small box=6.5kg

Answer 2

The weight of each large box is 15 kilograms, and each small box weighs 6 kilograms. This is determined by solving a system of linear equations representing the total weights of two different deliveries of boxes.

Let's denote the weight of each large box as L and the weight of each small box as S.

The given information can be translated into a system of linear equations:

1. For the delivery of 5 large boxes and 3 small boxes with a total weight of 87 kilograms:

5L + 3S = 87

2. For the delivery of 2 large boxes and 12 small boxes with a total weight of 105 kilograms:

2L + 12S = 105

Now, we can solve this system to find the values of L and S. One way to do this is by elimination or substitution.

Solving the system, we find that L = 15 kilograms and S = 6 kilograms.

Therefore, the weights are:

- Weight of each large box: 15 kilograms

- Weight of each small box: 6 kilograms