Question

A preschool teacher is rearranging four boxes of playing boxes so that each contains an equal number of blocks. Currently Box 1 has 32 blocks, Box 2 has 18, Box 3 has 41, and Box 4 has 9.

Select All the ways he could make each box have the same number of blocks.
A. Remove 7 blocks from Box 1 and place them in Box 2.
B. remove all the blocks and make four equal piles of 25, then put each pile in one of the boxes.
C. Remove 7 blocks from Box 1 and place them in box 2, and remove 16 blocks from Box 3 and place them in Box 4.
D. Remove 21 blocks from Box 3 and place them in Box 4
E. Remove 7 blocks from Box 1 and place them in Box 2, and remove 21 blocks from Box 3 and place them in Box 4.
Select ALL that apply
Have a good day/night!

Answer 1

The correct answers is B.

Explanation:

To make each box contain an equal number of blocks, we need to find the greatest common factor of the numbers 32, 18, 41, and 9.

The prime factors of each number are:

32 = 2^5

18 = 2 x 3^2

41 is a prime number

9 = 3^2

The greatest common factor is 1, which means it is not possible to make each box contain the same number of blocks by distributing the blocks among the boxes.

However, option B suggests removing all the blocks and making four equal piles of 25, then putting each pile in one of the boxes. This would give each box 25 blocks, which is a common factor of all the numbers.

Therefore, the correct answer is:

B. remove all the blocks and make four equal piles of 25, then put each pile in one of the boxes.