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
You're on a roll — Step 1: Determine the pattern using the second puzzle. In the second puzzle, we have the numbers: Star = 60, Left = 120, Triangle = 4, Right = ? Let the unknown right number be Y. We observe the pattern: (Left number) × (Triangle number) ÷ (Right number) = (Star number). Substitute the known values: 120 × 4 ÷ Y = 60 480 ÷ Y = 60 To solve for Y, we rearrange the equation: Y = (480)/(60) Y = 8 We can verify this pattern: 120 × 4 ÷ 8 = 480 ÷ 8 = 60. This matches the star number. Step 2: Solve the first puzzle using the established pattern. In the first puzzle, we have the numbers: Star = 80, Triangle = 10, Right = 12, Left = ? Let the unknown left number be X. Using the pattern: (Left number) × (Triangle number) ÷ (Right number) = (Star number). X × 10 ÷ 12 = 80 To solve for X: (10X)/(12) = 80 Simplify the fraction (10)/(12) to (5)/(6): (5X)/(6) = 80 Multiply both sides by 6: 5X = 80 × 6 5X = 480 Divide both sides by 5: X = (480)/(5) X = 96 The missing number in the blue box for the first puzzle is 96. Step 3: Solve the second puzzle using the established pattern. In the second puzzle, we have the numbers: Star = 60, Left = 120, Triangle = 4, Right = ? Let the unknown right number be Y. Using the pattern: (Left number) × (Triangle number) ÷ (Right number) = (Star number). 120 × 4 ÷ Y = 60 To solve for Y: 480 ÷ Y = 60 Y = (480)/(60) Y = 8 The missing number in the blue box for the second puzzle is 8. Got more? Send 'em!