a stack of firewood has 28 pieces on the bottom row,24 on the top of those,then 20 ,and so on.If there are 108 pieces of wood.How many rows are there?
Well, let's stack up some wood and do some math!
If we start with 28 pieces on the bottom row and subtract 4 for each row moving up, we can calculate the number of rows until we reach zero.
28, 24, 20, 16, 12, 8, 4, 0... Uh-oh, we ran out of wood before we reached 108 pieces.
It seems we made a little mistake here. With this pattern, it is impossible to have 108 pieces of wood. I guess someone has been sneaking wood away! Time to investigate the case of the disappearing firewood!🔎🕵️♂️
So, to answer your question, based on the given information, there is no possible number of rows that will give us 108 pieces of wood. I suggest you double-check those wood numbers!
To determine the number of rows, we need to find the pattern and sum the pieces of wood in each row until we reach a total of 108 pieces.
Let's analyze the pattern:
Bottom row: 28 pieces
Second row: 24 pieces (top of the previous row)
Third row: 20 pieces (top of the previous row)
...
We notice that each row decreases by 4 pieces from the previous row.
Let's calculate the sum of pieces in each row:
Row 1: 28 pieces
Row 2: 24 pieces (28 - 4)
Row 3: 20 pieces (24 - 4)
Row 4: 16 pieces (20 - 4)
Row 5: 12 pieces (16 - 4)
Row 6: 8 pieces (12 - 4)
To find the number of rows, we need to determine when the sum of these pieces reaches 108.
28 + 24 + 20 + 16 + 12 + 8 = 108
There are 6 rows in total.
To find the number of rows in the stack of firewood, we can follow these steps:
1. Let's start by analyzing the pattern. Each row has 4 fewer pieces of wood than the row below it. We can observe that the difference between the number of pieces between adjacent rows is decreasing by 4.
2. From the problem statement, we know that there are 108 pieces of wood in total. We need to determine the number of rows in the stack.
3. We can set up an equation to represent the relationship between the number of rows and the number of pieces of wood in the stack. Let's use (n) to represent the number of rows. The formula for the sum of an arithmetic series can be utilized here.
Sum of an arithmetic series = n/2 * (first term + last term)
4. The first term is given as 28, and the last term is the number of pieces on the top row. The difference between adjacent rows is 4, so the number of pieces on the top row would be 28 - (n-1)*4.
5. Therefore, substituting the values into the formula, we get:
108 = n/2 * (28 + 28 - (n-1)*4)
6. Simplify the equation:
108 = n/2 * (56 - 4n + 4)
7. Expanding the equation:
108 = n/2 * (60 - 4n)
8. Multiply both sides by 2 to remove the fraction:
216 = n * (60 - 4n)
9. Rearrange the equation and set it equal to zero:
4n^2 - 60n + 216 = 0
10. The equation is quadratic, so we can solve for n by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:
(n - 6)(4n - 36) = 0
11. Setting each factor equal to zero and solving for n, we get:
n - 6 = 0, which gives n = 6
4n - 36 = 0, which gives n = 9
12. Since the number of rows cannot be negative, we discard the solution n = 6.
13. Therefore, there are 9 rows in the stack of firewood.
well you could solve it the long way
28
24
20
16
12
8
4
add um all up=112
108 is 4 less so subtract the last row,
6 rows
there is some equation that is soposed to be faster, but seeing as all that took me 40 seconds aprox. WELL