Suppose the clerk had to stack 200 boxes of cereal in a triagle. How many boxes would be on the bottom row?
If each row has 1 more box than the row above, a stack n rows high has n(n+1)/2 boxes in it.
n(n+1)/2 = 200
n^2 + n - 400 = 0
n 19.5
So, the first 19 rows would have 190 boxes. Don't know what he'll do with the other 10.
To find the number of boxes on the bottom row of a triangle stack of cereal boxes, we need to determine the pattern.
In a triangle stack, the first row contains 1 box, the second row contains 2 boxes, the third row contains 3 boxes, and so on. This pattern follows the sequence of natural numbers.
We can notice that the number of boxes in each row follows a linear pattern. The first row has 1 box, the second row has 2 boxes, the third row has 3 boxes, and so on. So, the number of boxes in each row is equal to the row number.
To find the number of boxes on the bottom row, we need to determine the row number of the last row.
For a triangle stack with 200 boxes, we need to find the row number whose cumulative boxes will be equal to or just greater than 200.
We can start adding the number of boxes in each row until we reach a total of 200:
Row 1: 1 box (total so far: 1)
Row 2: 2 boxes (total so far: 3)
Row 3: 3 boxes (total so far: 6)
Row 4: 4 boxes (total so far: 10)
Row 5: 5 boxes (total so far: 15)
.
.
.
Row 13: 13 boxes (total so far: 91)
Row 14: 14 boxes (total so far: 105)
Row 15: 15 boxes (total so far: 120)
Row 16: 16 boxes (total so far: 136)
Row 17: 17 boxes (total so far: 153)
Row 18: 18 boxes (total so far: 171)
Row 19: 19 boxes (total so far: 190)
Row 20: 20 boxes (total so far: 210)
Here, we can see that the cumulative number of boxes in the rows exceeds 200 when we reach row 19. However, the cumulative number of boxes in the rows is less than 200 when we reach row 18.
Therefore, the bottom row of a triangle stack of 200 boxes of cereal would have 18 boxes.