An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed two small chandeliers and five large chandeliers, which had a total weight of 430 pounds. In the second box, he packed two small chandeliers and two large chandeliers, which had a weight of 196 pounds. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

A) Small chandelier: 70 pounds, Large chandelier: 90 pounds
B) Small chandelier: 60 pounds, Large chandelier: 100 pounds
C) Small chandelier: 80 pounds, Large chandelier: 110 pounds
D) Small chandelier: 50 pounds, Large chandelier: 120 pounds

The weight of a small chandelier is found to be 20 pounds, and the weight of a large chandelier is 78 pounds. However, this answer does not match any of the provided options.

Explanation:

To solve the problem, let's use a system of linear equations with two variables representing the weight of the small and large chandeliers. Let 's' be the weight of a small chandelier and 'l' be the weight of a large chandelier. From the information given, we can set up the following equations:

1. For the first box: 2s + 5l = 430

2. For the second box: 2s + 2l = 196

Now, let's solve the system of equations.

Multiply the second equation by 2.5 to align the coefficient of 'l' with the first equation:

2.5(2s + 2l) = 2.5(196)

5s + 5l = 490

Subtract the first equation from this result:

(5s + 5l) - (2s + 5l) = 490 - 430

3s = 60

s = 60 / 3

s = 20

Using the value of 's' in the second original equation:

2(20) + 2l = 196

40 + 2l = 196

2l = 196 - 40

2l = 156

l = 156 / 2

l = 78

So, each small chandelier weighs 20 pounds and each large chandelier weighs 78 pounds. However, this result does not match any of the options provided in the multiple-choice question.