Question

onnie is doing the office coffee run one morning. There are two coffee machines in the building: one from STACO and one from TRUCKBASS. They dispense two types of coffee: black (no milk) and white (with milk). The machines are both rather temperamental. Every fourth coffee dispensed from STACO is black and the rest are white. The coffees dispensed from TRUCKBASS are alternately black and white. Lonnie visited one of the machines and bought some coffees, of which three turned out to be white. He went back to the same machine for the afternoon run and bought the same number of coffees again. What are the possible numbers of white coffees that Lonnie could have received this time?

Answer 1

The possible numbers of white coffees that Lonnie could have received in the afternoon are 0 or 3.

Step-by-step explanation:

In this problem, Lonnie visited one of the coffee machines and bought some coffees, of which three turned out to be white. He then went back to the same machine for the afternoon run and bought the same number of coffees again. We need to determine the possible numbers of white coffees that Lonnie could have received this time.

Since every fourth coffee dispensed from STACO is black and the rest are white, we can conclude that every 3 out of 4 coffees from STACO are white. Therefore, if Lonnie received only white coffees in the morning, then it is possible that he could have received all black coffees in the afternoon.

On the other hand, the coffees dispensed from TRUCKBASS are alternately black and white. So, if Lonnie received three white coffees in the morning, it is not possible for him to receive all black coffees in the afternoon from TRUCKBASS.

Therefore, the possible numbers of white coffees that Lonnie could have received in the afternoon are 0 or 3, depending on which machine he visited.

Answer 2

Lonnie visited one of the machines and bought some coffees, of which three turned out to be white. That means Lonnie used STACO machine which pattern is giving 3 white every 1 black coffees.
He went back to the same machine for the afternoon and take another 3 coffees. Since the machine created 3 white in the morning, it should make 1 black coffee in the first run. The 2nd and 3rd run would give white coffee.

So, Lonnie will have 2 white coffee.