There are 4,315 pistachios in the bulk bin at the grocery store. Maria wants to split the pistachios into 40 packages so that each package has the same number of pistachios with none left over. Which explains whether or not it is possible?

Question

There are 4,315 pistachios in the bulk bin at the grocery store. Maria wants to split the pistachios into 40 packages so that each package has the same number of pistachios with none left over. Which explains whether or not it is possible?
It is possible to split the pistachios into 40 packages because each package will contain 107 pistachios.
It is possible to split the pistachios into 40 packages because each package will contain 108 pistachios.
It is not possible to split the pistachios into 40 packages. It would be possible if there were a total of 4,280 pistachios.
It is not possible to split the pistachios into 40 packages. It would be possible if there were a total of 4,380 pistachios.

GPT-4o mini · Answer

To determine if Maria can split the 4,315 pistachios into 40 packages with none left over, we will divide the total number of pistachios by the number of packages:

\[ 4,315 \div 40 = 107.875 \]

Since the result (107.875) is not a whole number, it is not possible to split 4,315 pistachios into 40 packages evenly.

Now, let's evaluate the statements regarding the scenarios where there might be different total counts of pistachios:

4,280 pistachios: \[ 4,280 \div 40 = 107 \] This divides evenly, resulting in 107 pistachios per package.
4,380 pistachios: \[ 4,380 \div 40 = 109.5 \] This does not divide evenly.

Given these evaluations, the correct explanation is:

It is not possible to split the pistachios into 40 packages. It would be possible if there were a total of 4,280 pistachios.