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 70 pounds. The truck is transporting 55 large boxes and 70 small boxes. If the truck is carrying a total of 4300 pounds in boxes, how much does each type of box weigh?​​

Answer 1

40 and 30 pounds

Explanation:

Let's call x the weight of the large box, and y the weight of the small box.

`\left \{ {{x+y=70} \atop {55x+70y=4300}} \right.`

Let's simplify the second by dividing by 5 first of all, and splitting the y term in two parts

`\left \{ {{x+y=70} \atop {11x+11y+3y=860}} \right.` Now let's replace the first into the second - after all, we have 11 times that.

`11(70) +3y = 860 \rightarrow 3y=90 \rightarrow y = 30` At this point we can use the first equation to easily see that
`x= 40`