Adelivery truck is transporting boxes of two sizes: large and small. the large boxes weigh 60 pounds each, and the small boxes weigh 35 pounds each. there are 110 boxes in all. if the truck is carrying a total of 5100 pounds in boxes, how many of each type of box is it carrying? number of large boxes: number of small boxes:

Let x=large boxes and y=small boxes.

x+y=110

60x+35y=5100

You need to cancel out one of the variables to solve for one. Let's cancel out y.

-35(x+y=110)

-35x-35y=-3850

60x+35y=5100

Add the two equations.

25x=1250

x=50

Plug in 50 for x into one of the equations to solve for y.

50+y=110

y=60

50 large boxes

60 small boxes

Set up a system of equations.

x+y=110

35x + 50y = 5100

Solve for a variable:

y=110-x

Plug this back into the other equation

35x + 50(110-x)=5100

Solve

35x + 5500 - 50x = 5100

-15x = -400

X = 26.66

Plug that into first equation to solve for y:

X+y=110

26.6+y=110

Y=110-26.6

Y=83.4

26.6 small boxes, 83.4 large