Question

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 1 small chandelier and 6 large chandeliers, which weighed a total of 193 kilograms. In the second box, he packed 1 small chandelier and 4 large chandeliers, which had a weight of 131 kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

Answer 1

The small chandelier weighs 7 kilograms and the large chandelier weighs 31 kilograms.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's denote the weight of a small chandelier as 'x' and the weight of a large chandelier as 'y'. From the information given, we can set up the following two equations:

1x + 6y = 193

1x + 4y = 131

We can now solve this system of equations using either substitution or elimination. Let's use the elimination method. Subtracting the second equation from the first equation, we get:

2y = 62

Dividing both sides by 2, we find that y = 31. Substitute this value of y into either of the original equations to find the weight of the small chandelier:

x + 4(31) = 131

x + 124 = 131

Subtracting 124 from both sides, we find that x = 7.

Therefore, the small chandelier weighs 7 kilograms and the large chandelier weighs 31 kilograms.