Kwan has modeled a number that is
less than 999. His model has twice
as many 100-blocks as 10-blocks.
It has twice as many 10-blocks as
1-blocks. What is the number?
421 or 842
That, of course, assumes there are no decimal points involved. Otherwise, the options are limitless.
if a 1 block means ones 10 block means tens and 100 block means 100s then the number would be 842 because 8 is 2 times as much as 4 and 4 is 2 times as much as 2
yeah 421 too
121
To solve this problem, we need to work backwards by considering the value of each block.
Let's assume the number of 1-blocks in Kwan's model is x.
According to the problem statement, Kwan's model has twice as many 10-blocks as 1-blocks. So, the number of 10-blocks would be 2x.
Similarly, the number of 100-blocks would be twice the number of 10-blocks, which is 2 * (2x) = 4x.
Now, we take into account the value of each type of block.
1-block = 1
10-block = 10
100-block = 100
To find the total value of Kwan's model, we multiply the number of each type of block by its respective value and add them together.
Total value = (1 * x) + (10 * 2x) + (100 * 4x)
Simplifying the equation:
Total value = x + 20x + 400x
Total value = 421x
Since the total value must be less than 999, we can set up an inequality:
421x < 999
Now we can solve for x:
x < 999/421
Dividing 999 by 421, we get:
x < 2.37
Since we're dealing with a whole number of blocks, x can only be either 2 or less.
Let's check the value for both cases:
If x = 1, then the total value would be:
Total value = 421 * 1 = 421
This is less than 999.
If x = 2, then the total value would be:
Total value = 421 * 2 = 842
This is also less than 999.
Therefore, the number that Kwan has modeled is either 421 or 842, depending on the number of 1-blocks.