Parmjit has 8 base ten blocks. She has at least one of each type of block. The value of her blocks is between 400 and 600. What blocks could she have? Find the possible answers using an organized list.
Ah, Parmjit and her colorful collection of base ten blocks! Let's see what she might have.
Since the value of her blocks is between 400 and 600, Parmjit must have a combination of blocks that adds up to a value within this range.
Now, let me get my clown calculator out and crunch some numbers.
To start, Parmjit could have 4 hundreds blocks, which would give her a value of 400.
If she adds one more tens block, that gives her another 100, making it 500.
But we're not done yet! Parmjit could also have another tens block and five ones blocks. That would give her a total of 600.
So the possible combinations of base ten blocks that Parmjit could have are:
- 4 hundreds, 0 tens, 0 ones (400)
- 3 hundreds, 1 tens, 0 ones (500)
- 3 hundreds, 0 tens, 5 ones (600)
Parmjit has some options there. I hope my organized list of possibilities brings a smile to your face!
To find the possible combinations, we need to consider the different types of base ten blocks and their values. Let's start by identifying the types of blocks Parmjit could have.
The base ten blocks consist of:
- Units (ones) block: 1
- Tens block: 10
- Hundreds block: 100
- Thousands block: 1000
Given that Parmjit has at least one of each type of block and a total of 8 blocks, we can use a systematic approach to find the possible combinations.
To create an organized list, we will allocate the blocks one by one, starting with the highest value blocks and moving down. Let's go step by step:
Step 1: Assume Parmjit has the thousands block (1000). In this case, she has 7 remaining blocks to distribute.
- Thousands block (1000): 1
- Remaining blocks: 7
Step 2: Decide how many hundreds blocks Parmjit could have. Since we want the total value of blocks to be between 400 and 600, Parmjit could have either 4, 5, or 6 hundreds blocks (100).
- Thousands block (1000): 1
- Hundreds blocks (100): 4, 5, or 6
- Remaining blocks: 7 - (4, 5, or 6) = 3, 2, or 1
Step 3: Consider the tens blocks. The remaining blocks could consist of any combination of tens blocks (10) that sums up to the value between 40 and 60.
- Thousands block (1000): 1
- Hundreds blocks (100): 4, 5, or 6
- Tens blocks (10): Any combination that sums to a value between 40 and 60
- Remaining blocks: 3, 2, or 1
Step 4: Calculate the remaining units blocks (ones). The remaining blocks could consist of any combination of units blocks (1) that sums up to the value between 4 and 6.
- Thousands block (1000): 1
- Hundreds blocks (100): 4, 5, or 6
- Tens blocks (10): Any combination that sums to a value between 40 and 60
- Units blocks (1): Any combination that sums to a value between 4 and 6
Using this systematic approach, we can generate an organized list of possible combinations considering the different types of blocks and their respective numbers.