Question

Compare the ratios 2:5
and 3:7
using the following tables. Finish the tables by filling in the missing values A and B. Which ratio is greater?

This table compares two sets of ratios, with the missing value A to be determined.
2 5
4 10
6 15
8 20
10 25
12 30
A 35
This table compares two sets of ratios, with the missing value B to be determined.
3 7
6 14
9 21
12 28
15 B
18 42
21 49

Answer 1

To compare the ratios 2:5 and 3:7, we'll first calculate the missing values A and B in the tables.

### For the first table (2:5):

The ratio 2:5 can also be expressed in terms of multiplication. For every increase of 2 in the first column (2, 4, 6, etc.), the corresponding increase in the second column follows the multiples of 5 (5, 10, 15, etc.).

The increment is 2 in the first column resulting in an increment of 5 in the second column.

Let's examine:
- 2 corresponds to 5
- 4 corresponds to 10
- 6 corresponds to 15
- 8 corresponds to 20
- 10 corresponds to 25
- 12 corresponds to 30
- A corresponds to 35

To find the missing value A, we follow the pattern:
- A corresponds to the first column value 14 (which is 12 + 2):

Using the ratio:
\[ 2 \div 5 = A \div 35 \]

To find A, we can check:
Since 35 is the double of 5, we can multiply the rest accordingly. The value of A must be doubled from 2 to get 14.

So we have:
- 14 corresponds to multiplied semi-prequisites of 7.

### For the second table (3:7):

For the second ratio, the pattern increases similarly.
- 3 corresponds to 7
- 6 corresponds to 14
- 9 corresponds to 21
- 12 corresponds to 28
- 15 corresponds to B
- 18 corresponds to 42

Looking at the values, we see:
- 3 × 5 = 15
- To find B in the second column:
B should correspond to \(7 \times 5 = 35\).

So, B = 35.

Now we have:

### Final Tables

1. First Table (2:5)
```
2 5
4 10
6 15
8 20
10 25
12 30
14 35 (A = 14)
```

2. Second Table (3:7)
```
3 7
6 14
9 21
12 28
15 35 (B = 35)
18 42
21 49
```

### Comparing Ratios

Now we can compare the values of these ratios:
- The ratio 2:5 simplifies to 0.4
- The ratio 3:7 simplifies to approximately 0.4285.

Since 0.4285 (3:7) is greater than 0.4 (2:5), we conclude:

**The ratio 3:7 is greater than the ratio 2:5.**