To determine if Hailey's estimate of making between 20 and 30 complete centerpieces is reasonable, we can divide the total number of flowers she has by the number of flowers needed for each centerpiece.
Hailey has a total of 430 flowers and each centerpiece requires 17 flowers.
We can perform the division:
\[ \frac{430}{17} \]
To calculate this, we can estimate it first. We know that:
- \( 17 \times 20 = 340 \)
- \( 17 \times 30 = 510 \)
This tells us that at 20 centerpieces, she would use 340 flowers, and at 30 centerpieces, she'd need 510 flowers. Since she has 430 flowers, the maximum number of centerpieces she can realistically make is between 20 and 30.
Now, let's perform the division explicitly:
Calculating \( 430 \div 17 \):
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Determine how many times 17 fits into 43 (the first two digits of 430):
- \( 17 \times 2 = 34 \) (this works)
- \( 17 \times 3 = 51 \) (this exceeds 43)
- So, 17 fits into 43 two times.
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Subtract 34 from 43:
- \( 43 - 34 = 9 \).
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Bring down the next digit from 430 (which is 0, making it 90):
- Now determine how many times 17 fits into 90:
- \( 17 \times 5 = 85 \) (this works)
- \( 17 \times 6 = 102 \) (this exceeds 90)
- So, 17 fits into 90 five times.
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Subtract 85 from 90:
- \( 90 - 85 = 5 \).
So, we find that:
\[ 430 \div 17 = 25 \text{ remainder } 5. \]
This means that Hailey can make 25 complete centerpieces using 17 flowers each, and she will have some flowers left over.
Conclusion:
Hailey's estimate of being able to make between 20 and 30 centerpieces is reasonable because she can actually make 25 centerpieces with the 430 flowers she has. Thus, her estimate falls within the correct range.
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