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?

2 5
4 10
6 15
8 20
10 25
12 30
A 35
3 7
6 14
9 21
12 28
15 B
18 42
21 49
(2 points)
Missing Value A =
. Missing Value B =
. The ratio
is greater.
Remaining Attempts : 3
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Answer 1

To fill in the missing values A and B in the provided tables, we first need to find the patterns in each ratio.

### For the ratio 2:5:

We can observe the pattern here:
- The first column is increasing by 2: 2, 4, 6, 8, 10, 12, A
- The second column is increasing by 5: 5, 10, 15, 20, 25, 30, 35

So we see that when the first column value increases by 2, the second column value increases by 5.

Therefore, if we continue this:
- When 12 (the last known value in the first column) + 2 = 14, then for the second column: 30 + 5 = 35
- Thus, A = 14.

### For the ratio 3:7:

We follow the same method:
- The first column is increasing by 3: 3, 6, 9, 12, 15, B
- The second column is increasing by 7: 7, 14, 21, 28, 35, 42, 49

Continuing this:
- When 15 (the last known value in the first column) + 3 = 18, then for the second column: 35 + 7 = 42
- Thus, B = 42.

Now we have:
- A = 14
- B = 42

### Final Comparison of Ratios 2:5 and 3:7:

To compare 2:5 and 3:7, we can convert the ratios to decimal form:

- 2:5 = 2/5 = 0.4
- 3:7 = 3/7 ≈ 0.4286

Since 0.4286 is greater than 0.4, we conclude:

Missing Value A = 14. Missing Value B = 42. The ratio 3:7 is greater.