Question

Consider the two patterns described below.
A
The terms in pattern W are 2 times the corresponding terms in pattern X.
B
The terms in pattern X are 8 less than the corresponding terms in pattern W.
C
The terms in pattern W are 8 less than the corresponding terms in patter X.
D
The terms in pattern X are 2 times the corresponding terms in pattern W.

Answer 1

Let's analyze the relationships between the terms in patterns W and X based on the given descriptions:

1. **A**: The terms in pattern W are 2 times the corresponding terms in pattern X.
- This can be expressed as:
\( W = 2X \)

2. **B**: The terms in pattern X are 8 less than the corresponding terms in pattern W.
- This can be expressed as:
\( X = W - 8 \)

3. **C**: The terms in pattern W are 8 less than the corresponding terms in pattern X.
- This can be expressed as:
\( W = X - 8 \)

4. **D**: The terms in pattern X are 2 times the corresponding terms in pattern W.
- This can be expressed as:
\( X = 2W \)

Now, let’s analyze these relationships further to see if they are consistent.

### From A and B:
If we substitute \( W = 2X \) from A into B:
- Using B: \( X = W - 8 \)
- Substitute \( W \):
\( X = 2X - 8 \)
\( 0 = X - 8 \)
\( X = 8 \)

Using \( X = 8 \) in A:
\( W = 2(8) = 16 \)

### Check C:
Substituting \( X = 8 \) into C should also hold:
\( W = X - 8 \)
\( W = 8 - 8 = 0 \)
This gives inconsistent values, so A and B cannot be correct together.

### Check D:
From D, if we take \( X = 2W \):
Substituting \( 2W = W - 8 \) from B:
\( 2W = W - 8 \)
This leads to \( W = 8 \) and \( X = 16 \).

The relationships are contradictory in combinations.

In summary:
- A and D are one pair of pairing options.
- B and C would be inconsistent with other's outcome values.

So only the terms of A and D can represent consistent relationships, as B and C conflict with those value pairs. In conclusion, patterns match only on specific descriptions A and D.