To determine if Hailey's estimate of being able to make between 20 and 30 complete centerpieces is reasonable, we can start by calculating how many centerpieces she can actually make with the 430 flowers she has.
To find the number of centerpieces, we divide the total number of flowers by the number of flowers per centerpiece:
\[ \text{Number of centerpieces} = \frac{\text{Total flowers}}{\text{Flowers per centerpiece}} = \frac{430}{17} \]
Now we can perform the division:
- First, we can simplify our calculation by estimating \( \frac{430}{17} \).
- We know that \( 17 \) is approximately \( 20 \) when we are considering the range defined by Hailey (20 to 30 centerpieces). To get a rough estimate:
\[ \frac{430}{20} = 21.5 \]
- Next, we can check for \( \frac{430}{30} \):
\[ \frac{430}{30} \approx 14.33 \]
This means Hailey could make around 21.5 centerpieces if each requires 20 flowers, and about 14 if it requires 30. This shows the actual possible centerpieces will lie between 14 and 21.
Now let's calculate the exact value of \( \frac{430}{17} \):
-
By performing the division:
- 17 goes into 43 two times (since \( 17 \times 2 = 34 \)), leaving a remainder of \( 43 - 34 = 9 \).
- Bring down the next digit (0), making it 90.
- 17 goes into 90 five times (since \( 17 \times 5 = 85 \)), with a remainder of \( 90 - 85 = 5 \).
- Bring down the next digit (0) again, making it 50.
- 17 goes into 50 two times (since \( 17 \times 2 = 34 \)), with a remainder of \( 50 - 34 = 16 \).
- Bringing down another \( 0 \), you get 160.
- 17 goes into 160 nine times (since \( 17 \times 9 = 153 \)), with a remainder of 7.
So, \( 430 \div 17 \approx 25.29 \).
Thus, the maximum number she can make is realistically around 25 complete centerpieces.
Conclusion for Part A: Hailey's estimate of being able to make between 20 to 30 centerpieces is reasonable because the actual calculation shows she can make about 25 centerpieces, which falls within her estimated range.
Part B Was there any mistake in her estimation? If so, explain what she might have neglected to consider when estimating the number of centerpieces she could create.
Hailey’s initial estimate appears to be somewhat optimistic since she estimated she could make between 20 and 30 centerpieces, while a more accurate calculation shows she can realistically make around 25 centerpieces.
What might she have neglected?
-
Exact Division: She may have underestimated how strict the division of flowers per centerpiece should be since the actual calculation yields a number that indicates she cannot make 30 centerpieces with the 430 flowers.
-
Rounding: She may have rounded her count of centerpieces casually without recalculating precisely. She may have assumed that if 17 flowers fit into 400 easily, she could include the additional 30 flowers to make 30 centerpieces, neglecting the specific ratio.
-
Waste or Damage: She might not have factored in any potential waste or the possibility that some flowers might not be usable due to damage or other quality issues, meaning she could end up with fewer complete centerpieces than she anticipates.
In summary, her initial estimate was slightly optimistic, and she may have neglected to consider the exact division and the practical implications of using flowers, leading to her broader initial range.
1 answer