Question

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he

packed 4 small chandeliers and 6 large chandeliers, which weighed a total of 530 pounds. In the second box,
he packed 4 small chandeliers and 4 large chandeliers, which had a weight of 392 pounds. Assuming the
weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

Answer 1

By setting up and solving a system of equations, we determined that each small chandelier weighs 29 pounds and each large chandelier weighs 69 pounds.

Step-by-step explanation:

To solve for the weight of each size of chandelier, we can set up a system of two equations based on the two scenarios provided:

Let x be the weight of a small chandelier and y be the weight of a large chandelier.

1. 4x + 6y = 530
2. 4x + 4y = 392

Now we solve the system of equations:

Step 1: Subtract the second equation from the first to eliminate x and find the weight of y.

1. 4x + 6y - (4x + 4y) = 530 - 392
2. 2y = 138
3. y = 69 pounds

Step 2: Substitute y into one of the original equations to solve for x.

1. 4x + 4(69) = 392
2. 4x + 276 = 392
3. 4x = 116
4. x = 29 pounds

Therefore, each small chandelier weighs 29 pounds and each large chandelier weighs 69 pounds.

Answer 2

large chandeliers = 69 pounds

small chandeliers = 29 pounds