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.

Explanation:

Identify the given values and goal

Using the Divisibility knowledge point
We need to determine if \(4,315\) pistachios can be divided equally into \(40\) packages with no remainder.

• Total pistachios: \(4,315\)
• Number of packages: \(40\)

Perform the division

Using the Long Division Steps knowledge point

$$ 4315 \div 40 = 107 \text{ R } 35 $$

Since there is a remainder of \(35\), it is not possible to split them evenly.

Find the nearest divisible numbers

Using the Divisibility knowledge point

$$
LATEXBLOCK0
$$

A total of \(4,280\) pistachios would allow an even split of \(107\) per package.

Match with the given options

Using the Divisibility knowledge point

• Option 1: It is possible... (Incorrect, there is a remainder)
• Option 2: It is possible... (Incorrect, there is a remainder)
• Option 3: It is not possible... It would be possible if there were a total of 4,280 pistachios. (Correct, \(4280 \div 40 = 107\))
• Option 4: It is not possible... It would be possible if there were a total of 4,380 pistachios. (Incorrect, \(4380 \div 40 = 109.5\))

Answer:

• (A) It is possible to split the pistachios into 40 packages because each package will contain 107 pistachios.
• (B) It is possible to split the pistachios into 40 packages because each package will contain 108 pistachios.
• (C) It is not possible to split the pistachios into 40 packages. It would be possible if there were a total of 4,280 pistachios. (Correct answer)
• (D) It is not possible to split the pistachios into 40 packages. It would be possible if there were a total of 4,380 pistachios.