Consider the two patterns described below.

Question

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.