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Problem of the Week
Problem A and Solution
Delivery Dilemma

Problem

At the beginning of the day, a delivery truck contains \(368\) packages.
The driver of the truck is making deliveries to various office buildings in a city.

When the drivers returns to the depot for a lunch break, \(273\) packages are added to the truck.

At \(4\) p.m., they have \(99\) packages left in the truck. How many packages did they deliver between \(3\) p.m. and \(4\) p.m.?

Solution

Since they start with \(368\) packages in the truck, at \(10\) a.m. they will have \(368 - 66 = 302\) packages in the truck.
Then at \(11\) a.m. they will have \(302 - 103 = 199\) packages in the truck, and at \(12\) p.m. they will have \(199 - 88 = 111\) packages in the truck.

At lunch they add \(273\) packages to the truck, so there are now \(111 + 273 = 384\) packages in the truck.

Thus, in the afternoon, they start with \(384\) packages in the truck.
Then at \(2\) p.m. they will have \(384 - 111 = 273\) packages in the truck, and at \(3\) p.m. they will have \(273 - 86 = 187\) packages in the truck.

Since there are \(99\) packages on the truck at \(4\) p.m., then there must have been \(187 - 99 = 88\) packages delivered between \(3\) p.m. and \(4\) p.m.