An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 2 small chandeliers and 6 large chandeliers, which weighed a total of 134 kilograms. In the second box, he packed 5 small chandeliers and 6 large chandeliers, which had a weight of 155 kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?
If there are x small and y large, then
2x + 6y = 134
5x + 6y = 155
subtract
3x = 21
now finish it off
To find the weight of each size of chandelier, let's assign variables to the unknown weights. Let's call the weight of a small chandelier "x" and the weight of a large chandelier "y".
From the information given, we can create two equations:
1. 2x + 6y = 134
2. 5x + 6y = 155
We now have a system of equations. We'll use a method called substitution to solve for x and y.
1. Let's solve equation 1 for x:
2x + 6y = 134
2x = 134 - 6y
x = (134 - 6y) / 2
x = 67 - 3y
2. Now, substitute the value of x in equation 2:
5x + 6y = 155
5(67 - 3y) + 6y = 155
335 - 15y + 6y = 155
-9y = 155 - 335
-9y = -180
y = -180 / -9
y = 20
3. Substitute the value of y back into equation 1 to find x:
x = 67 - 3y
x = 67 - 3(20)
x = 67 - 60
x = 7
Therefore, a SMALL chandelier weighs 7 kilograms, and a LARGE chandelier weighs 20 kilograms.