A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40

 pounds each, and the small boxes weigh 15

 pounds each. There are 120

 boxes in all. If the truck is carrying a total of 3175

 pounds in boxes, how many of each type of box is it carrying?

Let the number of box of large size be x

And

the number of box of small size be y

We are given that total number of boxes are 120

So we have

x+y=120 ----->(1)

Now

We have

large boxes weigh 40

 pounds each

So x boxes of large size weight 40x

and

the small boxes weigh 15 pounds each

So

y boxes of small size weigh 15y

We have that total wieght is 3175

So

40x+15y=3175 ----->(2)

Now we have two equation (1) and (2)

Now we use these to solve for x and y

From (1)

x+y=120

We get

x=120-y

Putting this in (2)

We get

40(120-y)+15y=3175

4800-40y+15y=3175

-25y=3175-4800

-25y=-1625

y=?−25−1625??

y=65

Now putting y=65 in x=120-y

We get x=120-65

x=55

So number of box of large size =55

And number of box of small size=65