What are the answers to Questions 18, 19, and 20 regarding square tiles, number patterns, and reciprocals?

The floor of a room was covered by 2916 square tiles. This means the area of the floor is 2916 square tiles. Since it's a square floor, the number of tiles along each side is the square root of the total number of tiles.

$$\text{Number of tiles per side} = \sqrt{2916}$$

To find the square root of 2916:
We can estimate: $50^2 = 2500$ and $60^2 = 3600$. So the answer is between 50 and 60.
The last digit of 2916 is 6, so the square root must end in 4 or 6.
Let's try $54^2$:

$$54 \times 54 = 2916$$

So, there were 54 square tiles along each side of the floor.

The final answer is $\boxed{\text{A. } 54}$.

The given number pattern is $5, 11, 23, 47, 95, \dots$
Let's find the difference between consecutive terms:
$11 - 5 = 6$
$23 - 11 = 12$
$47 - 23 = 24$
$95 - 47 = 48$
The differences are $6, 12, 24, 48$. This sequence of differences is doubling each time ($6 \times 2 = 12$, $12 \times 2 = 24$, $24 \times 2 = 48$).
The next difference should be $48 \times 2 = 96$.
To find the next number in the pattern, add this difference to the last term:

$$95 + 96 = 191$$

The next number in the pattern is 191.

The final answer is $\boxed{\text{D. } 191}$.

We need to write the reciprocal of $2\frac{2}{5}$.
First, convert the mixed number to an improper fraction:

$$2\frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$$

The reciprocal of a fraction is obtained by inverting the numerator and the denominator.
The reciprocal of $\frac{12}{5}$ is $\frac{5}{12}$.

The final answer is $\boxed{\text{D. } \frac{5}{12}}$.

Hassan bought $5\frac{5}{7}$ kg of meat and Abdan bought $4\frac{1}{4}$ kg of meat.
To find the total fraction of meat they bought altogether, add the two amounts:

$$5\frac{5}{7} + 4\frac{1}{4}$$

Add the whole numbers and the fractions separately:

$$5 + 4 = 9$$

Now add the fractions:

$$\frac{5}{7} + \frac{1}{4}$$

Find a common denominator for 7 and 4, which is 28.

$$\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}$$ $$\frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}$$

Now add the converted fractions:

$$\frac{20}{28} + \frac{7}{28} = \frac{20 + 7}{28} = \frac{27}{28}$$

Combine the whole number and the fraction:

$$9 + \frac{27}{28} = 9\frac{27}{28}$$

The total amount of meat bought is $9\frac{27}{28}$ kg.
Looking at the options, none of them exactly match $9\frac{27}{28}$. Let's recheck the calculation.
The options are given as improper fractions or mixed numbers with different denominators.
Let's convert $9\frac{27}{28}$ to an improper fraction:

$$9\frac{27}{28} = \frac{(9 \times 28) + 27}{28} = \frac{252 + 27}{28} = \frac{279}{28}$$

Let's check the options provided.
Option B is $9\frac{1}{21}$. This is $\frac{(9 \times 21) + 1}{21} = \frac{189+1}{21} = \frac{190}{21}$.
Option D is $9\frac{6}{10}$. This is $9\frac{3}{5} = \frac{(9 \times 5) + 3}{5} = \frac{45+3}{5} = \frac{48}{5}$.
Option A is $10\frac{21}{22}$.
Option C is $10\frac{1}{21}$.
It seems there might be a slight discrepancy in the options or the question's intended answer. However, based on the calculation, $9\frac{27}{28}$ is the correct sum.
Let's re-examine the options and the question. The question asks "What fraction of meat did they buy altogether?".
If we assume a typo in the options and that $9\frac{27}{28}$ should be an option, then that would be the answer.
Let's check if any option is close or if there's a common mistake.
$9\frac{27}{28}$ is very close to 10.
Let's check the options again.
A. $10\frac{21}{22}$
B. $9\frac{1}{21}$
C. $10\frac{1}{21}$
D. $9\frac{6}{10}$
None of the options match $9\frac{27}{28}$.
Let's re-calculate to ensure no arithmetic error.
$5\frac{5}{7} + 4\frac{1}{4} = (5+4) + (\frac{5}{7} + \frac{1}{4}) = 9 + (\frac{20}{28} + \frac{7}{28}) = 9 + \frac{27}{28} = 9\frac{27}{28}$.
The calculation is correct. Given the multiple-choice format, there might be an error in the question's options.
However, if forced to choose the closest option, $9\frac{27}{28}$ is approximately 9.96.
$10\frac{21}{22} \approx 10.95$
$9\frac{1}{21} \approx 9.04$
$10\frac{1}{21} \approx 10.04$
$9\frac{6}{10} = 9.6$
None of the options are particularly close to 9.96.
Let's assume there was a typo in the question and one of the fractions was different.
If the question was $5\frac{5}{7} + 4\frac{1}{7} = 9\frac{6}{7}$.
If the question was $5\frac{5}{7} + 4\frac{1}{21} = 9 + \frac{15}{21} + \frac{1}{21} = 9\frac{16}{21}$.
Given the options, it's possible there's a mistake in the question or options.
However, I must provide an answer from the given options.
Let's re-evaluate the problem and options.
The sum is $9\frac{27}{28}$.
Let's check if any option is a simplified form or an equivalent fraction. No.
Let's consider if the question meant something else, e.g., multiplication, but it clearly says "altogether".
Since I must choose an option, and my calculation is $9\frac{27}{28}$, which is not an option, I will state that the calculated answer is not among the options. However, as per instructions, I must select an option. This implies there's an error in the question or options.
Let's assume the question intended for a result that simplifies to one of the options.
If the answer was $10\frac{1}{21}$, it would mean the sum was $10 + \frac{1}{21} = \frac{210+1}{21} = \frac{211}{21}$.
If the answer was $9\frac{1}{21}$, it would mean the sum was $9 + \frac{1}{21} = \frac{189+1}{21} = \frac{190}{21}$.
Let's re-read the question carefully. "What fraction of meat did they buy altogether?"
The calculation $9\frac{27}{28}$ is correct.
Given the constraint to select an option, and the fact that $9\frac{27}{28}$ is very close to 10, let's consider the options that are close to 10.
$10\frac{21}{22}$ is approximately 10.95.
$10\frac{1}{21}$ is approximately 10.04.
$9\frac{27}{28} \approx 9.964$.
$10\frac{1}{21}$ is the closest option to $9\frac{27}{28}$ if we round $9\frac{27}{28}$ up to 10 and then consider fractions.
This is a problematic question due to the options. I will state the correct calculation and then choose the closest option, noting the discrepancy.

The sum is $9\frac{27}{28}$. This is not directly available in the options.
However, if we consider the options, $10\frac{1}{21}$ is approximately 10.047, and $9\frac{27}{28}$ is approximately 9.964. These are quite close. It's possible there was a rounding or simplification error in the question's options.
Given the options, and the fact that $9\frac{27}{28}$ is very close to 10, option C ($10\frac{1}{21}$) is the closest value among the options that are greater than 9.
Let's assume there was a slight error in the question or options and choose the closest one.
The difference between $10\frac{1}{21}$ and $9\frac{27}{28}$ is $10\frac{1}{21} - 9\frac{27}{28} = \frac{211}{21} - \frac{279}{28} = \frac{211 \times 4 - 279 \times 3}{84} = \frac{844 - 837}{84} = \frac{7}{84} = \frac{1}{12}$.
The difference between $9\frac{27}{28}$ and $9\frac{1}{21