Question

The bed of a truck is stacked with with boxes of paper. The boxes are stacked 5 boxes deep by 4 boxes high by 4 boxes across

When the driver is in the truck, the mass is 2948.35 Kilograms.
The mass of 1 box of paper is 22.5 Kilograms
The driver delivers some of the boxes of paper at his first stop.
The truck has to drive over a bridge on the way to the next stop.
Trucks with a mass greater than 4700 kilograms are not allowed over the bridge

What is tue minimum number of boxes of paper the driver must deliver at the first stop to be allowed to drive over the bridge

Answer 1

3

Explanation:

The boxes are stacked 5 boxes deep by 4 boxes high by 4 boxes across, then there are
`5\cdot 4\cdot 4=80` boxes in total.

The mass of 1 box of paper is 22.5 kilograms, so 80 boxes weigh
`22.5\cdot 80=1800` kilograms.

When the driver is in the truck, the mass is 2948.35 kilograms, then the total mass is

`2948.35+1800=4748.35\ kg.`

Let n be the number of boxes of paper the driver must deliver at the first stop. Their weigth is 22.5n kg and the weight of the truck without n boxes is

`4748.35-22.5n\ kg.`

Trucks with a mass greater than 4700 kilograms are not allowed over the bridge, thus

`4748.35-22.5n<4700,\\ \\22.5n>48.35,\\ \\n>(967)/(450)=2(67)/(450).`

Hence, the driver must deliver at least 3 boxes at the first shop.