This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Analyze the given information. The diagram shows an input, a first rule (unknown, marked with "?"), a second rule (÷ 3), and a final output. We need to find the missing rule in the first box. We have the following input-output pairs: • Input 24, Output 6 • Input 39, Output 11 • Input 54, Output 16 • Input 18, Output 4 • Input 45, Output 13 • Input 12, Output (missing) Step 2: Determine the intermediate values by reversing the second rule. The second rule is "÷ 3". To find the value before this rule was applied (the intermediate value), we multiply the output by 3. • For Input 24, Output 6: Intermediate Value = 6 × 3 = 18. • For Input 39, Output 11: Intermediate Value = 11 × 3 = 33. • For Input 54, Output 16: Intermediate Value = 16 × 3 = 48. • For Input 18, Output 4: Intermediate Value = 4 × 3 = 12. • For Input 45, Output 13: Intermediate Value = 13 × 3 = 39. Step 3: Find the first rule by comparing inputs and intermediate values. Now we look at the relationship between the original Input and the Intermediate Value: • Input 24 Intermediate Value 18 • Input 39 Intermediate Value 33 • Input 54 Intermediate Value 48 • Input 18 Intermediate Value 12 • Input 45 Intermediate Value 39 In each case, the Intermediate Value is 6 less than the Input. 24 - 6 = 18 39 - 6 = 33 54 - 6 = 48 18 - 6 = 12 45 - 6 = 39 Therefore, the missing rule in the first box is "-6". The missing rule is -6. That's 2 down. 3 left today — send the next one.