Question

4. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 1 small chandelier and 5 large chandeliers, which weighed a total of 261 pounds. In the second box, he packed 2 small chandeliers and 2 large chandeliers, which had a weight of 130 pounds. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh? Each small chandelier weighs (3 Points) pounds and each large one weighs pounds.

Answer 1

First box:

1 small chandelier

5 large chandeliers

Total weight = 261

Equation:

1x+5y= 261 (a)

Where

x = weight of each small chandelier

y= weight of each ñarge chandelier

Second box:

2 small chandeliers

2 large chandeliers

130 pounds

2x+2y= 130 (b)

System of equations:

1x+5y= 261 (a)

2x+2y= 130 (b)

Multiply (a) by 2 and subtract (b) to (a)

2x+10y= 522

-

2x+2y= 130

___________

8y= 392

Solve for y

y= 392/8

y= 49

Replace y on (a) or (b) and solve for x

1x+5y= 261 (a)

x+5(49)=261

x+245=261

x=261-245

x= 16

Each small chandelier weighs 16 pounds and each large one weighs 49 pounds.​