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 75 pounds. The truck is transporting 70

large boxes and 65 small boxes. If the truck is carrying a total of 5075
pounds in boxes, how much does each type of box weigh?

Answer 1

large box weights 40 pounds & small box weights 35 pounds

Explanation:

We can write 2 equations and solve simultaneous.

Let x be weight of large box and y be weight of small box

"The combined weight of a large box and a small box is 75 pounds.":

`x+y=75`

"The truck is transporting 70 large boxes and 65 small boxes. If the truck is carrying a total of 5075 pounds":

`70x+65y=5075`

Now we can solve for x in the first equation, which is x = 75 -y

We now substitute this into the 2nd equation and solve for y:

`70x+65y=5075\\70(75-y)+65y=5075\\5250-70y+65y=5075\\-5y=5075-5250\\-5y=-175\\y=35`

Using y = 35 and plugging that into the 1st equation, we can solve for x:

`x+y=75\\x+35= 75\\x= 75 - 35\\x=40`

Hence, large box weights 40 pounds & small box weights 35 pounds