To find the missing values A and B in the tables, we need to maintain the same ratio for each row as defined by the ratios 7:4 and 12:5.
Starting with the first ratio 7:4, we can determine that:
- For every 7 in the first column, there is a corresponding 4 in the second column.
Let's establish the constant (k) for the ratios:
- \( k = \frac{7}{4} \)
Now we can fill in values for A and B based on the second table with ratio 12:5, where we want to determine how many times the base ratio fits.
From the given values, we see that:
For the first table (7:4):
- 7 corresponds to 4, 14 corresponds to 8, and so on, maintaining the ratio.
- If we continue the pattern, we see each row multiplies the first number by 1 (7, 14, 21, 28) and applies the ratio to get the second column (4, 8, 12, 16).
Following this, we can find A:
- \( 7x = A \) and must fit the same ratio as the last entry:
- If we take the next multiple that fits the table's pattern, \( A \) should be \( 7 \times 5 = 35 \) while following up on \( B \) through the proportion to maintain \( 4 \).
Now, to find B:
- Using the same method on the second table (12:5):
- If \( B = 5n \), we look to find which row fits into the ratio.
- We compute: \[ A: (k) = \frac{12x}{5} \] Plugging in \( A = 35 \): \[ A = 35 \rightarrow A = 7 \cdot 5 = 35 \quad \text{and} \quad B = \frac{5}{12} \cdot 35 \]
To solve B:
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\( 35 \times \frac{5}{12} = \frac{175}{12} = 14.5833, so we round that to fit the table and print as per integer values matching ( \frac{7}{4} \) style.
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Check:
- Ratios commonly denotes both perspectives \( 7:4 \) and \( 12:5 \)
- We see A is clearly 35 aligning downtrodden back to multiple involved rows.
Thus, B rounds to values closely to 20 to maintain consistency per aligned ratios.
Hence we determine:
- \( A = 35 \)
- \( B = 20 \)
Therefore, the correct option is: A = 35 and B = 20.