word problem and linear equations

Question

A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is
80
pounds. The truck is transporting
65
large boxes and
55
small boxes. If the truck is carrying a total of
4850
pounds in boxes, how much does each type of box weigh?

Answer 1

55 large paired with 55 small = 55 * 80 = 4400 lbs

4850 - 4400 = 450 lbs

The unpaired 10 large boxes then weigh 450 lbs, or 45 lbs each.  80 - 45 = 35 lbs for the small boxes.

Answer 2

x =weight of small box

y = weight of large box

 

x + y = 80

55x + 65y = 4850

 

Multiply first equation by 55

 

55x + 55y = 4400

55x + 65y = 4850

 

Subtract 

 

10y = 450

 

y= 45 lb

x= 35 lb