An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 2 small chandeliers and 5 large chandeliers, which weighed a total of 432 pounds. In the second box, he packed 6 small chandeliers and 3 large chandeliers, which had a weight of 360 pounds. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?
Let's say the weight of a small chandelier is x pounds and the weight of a large chandelier is y pounds.
In the first box, the weight of 2 small chandeliers is 2x pounds and the weight of 5 large chandeliers is 5y pounds. This means that 2x + 5y = 432.
In the second box, the weight of 6 small chandeliers is 6x pounds and the weight of 3 large chandeliers is 3y pounds. This means that 6x + 3y = 360.
We can solve this system of equations by either substitution or elimination. Let's use substitution.
From the first equation, we can express x in terms of y: x = (432 - 5y)/2.
Substituting this into the second equation, we get: 6((432 - 5y)/2) + 3y = 360.
Multiplying through by 2 to eliminate the fraction, we have: 6(432 - 5y) + 6y = 720.
Expanding and combining like terms, we get: 2592 - 30y + 6y = 720.
Combining like terms again, we get: -24y = -1872.
Dividing by -24, we find that y = 78.
Substituting this back into the first equation, we get: 2x + 5(78) = 432.
Simplifying, we find: 2x + 390 = 432.
Subtracting 390 from both sides, we get: 2x = 42.
Dividing by 2, we find that x = 21.
Therefore, the weight of a small chandelier is 21 pounds and the weight of a large chandelier is 78 pounds.