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 70large boxes and 65 small boxes. If the truck is carrying a total of 5075pounds in boxes, how much does each type of box weigh?

Answer:large box weights 40 pounds & small box weights 35 poundsStep-by-step 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.":[tex]x+y=75[/tex]"The truck is transporting 70  large boxes and 65 small boxes. If the truck is carrying a total of 5075  pounds":[tex]70x+65y=5075[/tex]Now we can solve for x in the first equation, which is x = 75 -yWe now substitute this into the 2nd equation and solve for y:[tex]70x+65y=5075\\70(75-y)+65y=5075\\5250-70y+65y=5075\\-5y=5075-5250\\-5y=-175\\y=35[/tex]Using y = 35 and plugging that into the 1st equation, we can solve for x:[tex]x+y=75\\x+35= 75\\x= 75 - 35\\x=40[/tex]Hence, large box weights 40 pounds & small box weights 35 pounds