ou just found three rules that give you an output of 7 when the input is 12. Now, here are some more input-output pairs in the table. Which rule would make all of these input-output pairs true?

Question

input
Input Output Arrow
rule
Input Output Arrow
ouput

Input Output
12 7
24 19
9 4
16 11

Divide by 2, then add 1.

Add 2, then divide by 2.

Subtract 5.

Answer 1

Let's analyze the given input-output pairs and see which of the proposed rules fits all of them.

Here are the given pairs:

1. 12 → 7
2. 24 → 19
3. 9 → 4
4. 16 → 11

Now, let's assess each rule:

Rule 1: Divide by 2, then add 1.

• For 12:
  \( \frac{12}{2} + 1 = 6 + 1 = 7 \) (Correct)

• For 24:
  \( \frac{24}{2} + 1 = 12 + 1 = 13 \) (Incorrect)

• For 9:
  \( \frac{9}{2} + 1 = 4.5 + 1 = 5.5 \) (Incorrect)

• For 16:
  \( \frac{16}{2} + 1 = 8 + 1 = 9 \) (Incorrect)

Rule 2: Add 2, then divide by 2.

• For 12:
  \( \frac{12 + 2}{2} = \frac{14}{2} = 7 \) (Correct)

• For 24:
  \( \frac{24 + 2}{2} = \frac{26}{2} = 13 \) (Incorrect)

• For 9:
  \( \frac{9 + 2}{2} = \frac{11}{2} = 5.5 \) (Incorrect)

• For 16:
  \( \frac{16 + 2}{2} = \frac{18}{2} = 9 \) (Incorrect)

Rule 3: Subtract 5.

• For 12:
  \( 12 - 5 = 7 \) (Correct)

• For 24:
  \( 24 - 5 = 19 \) (Correct)

• For 9:
  \( 9 - 5 = 4 \) (Correct)

• For 16:
  \( 16 - 5 = 11 \) (Correct)

Conclusion

The only rule that makes all the input-output pairs true is the third rule: Subtract 5.