Question

A toddler has 36 blocks, of which 16 are blue and 20 are pink. They want to sort the blocks so that each group has both colors of blocks. The toddler also wants each group to have an equal number of blue blocks and an equal number of pink blocks. Which answer best shows how the toddler should sort the blocks using the greatest common factor (GCF) and the distributive property of multiplication over addition?

1) 2(8b + 10p)
2) 4(4b + 5p)
3) 6(2b + 3p)
4) 8(b + 2p)

Answer 1

To sort the blocks, we need to find the GCF and use the distributive property. The answer is 4(4b + 5p).

Step-by-step explanation:

To sort the blocks so that each group has both colors of blocks and an equal number of blue and pink blocks, we need to find the greatest common factor (GCF) of the number of blue and pink blocks. In this case, the GCF of 16 and 20 is 4.

Using the distributive property of multiplication over addition, we can express the total number of blocks as 4(4b + 5p), where b represents blue blocks and p represents pink blocks.

Therefore, the answer is option 2) 4(4b + 5p).

Answer 2

The toddler can sort the blocks into groups using the greatest common factor of 4, resulting in the expression 4(4b + 5p), which indicates 4 groups of 4 blue and 5 pink blocks each.

Step-by-step explanation:

To solve this problem, we must use the greatest common factor (GCF) and the distributive property of multiplication to group the blocks into sets with equal numbers of blue and pink blocks.

We start by determining the GCF of the number of blue blocks (16) and pink blocks (20), which is 4. The distributive property of multiplication over addition then allows us to express the total number of blocks in terms of this GCF.

The toddler can sort the blocks into 4 groups of 4 blue blocks and 5 pink blocks each, resulting in the expression 4(4b + 5p), where b represents a blue block and p represents a pink block.