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
The problems follow two patterns, derived from the examples: 1. The sum of the number in the top-left corner and the number in the bottom-right corner equals the number in the outside box. Top-Left + Bottom-Right = Outside Box 2. The number in the bottom-left corner is twice the number in the top-right corner. Bottom-Left = 2 × Top-Right Let's solve each problem: Problem 11: Given: Top-Left = 18, Top-Right = 20, Bottom-Left = 36, Outside Box = 50. Missing: Bottom-Right. Using Pattern 1: 18 + Bottom-Right = 50 Bottom-Right = 50 - 18 Bottom-Right = 32 (Note: Pattern 2, 36 = 2 × 20, is not true for this problem, so we only use Pattern 1 for the missing value.) Your answer of 30 is incorrect. The missing number is 32. Problem 12: Given: Top-Left = 82, Bottom-Left = 28, Bottom-Right = 63, Outside Box = 145. Missing: Top-Right. Using Pattern 2: 28 = 2 × Top-Right Top-Right = (28)/(2) Top-Right = 14 (Note: Pattern 1, 82 + 63 = 145, is consistent with the given outside box.) The missing number is 14. Problem 13: Given: Top-Left = 42, Top-Right = 50, Bottom-Left = 11, Outside Box = 53. Missing: Bottom-Right. Using Pattern 1: 42 + Bottom-Right = 53 Bottom-Right = 53 - 42 Bottom-Right = 11 (Note: Pattern 2, 11 = 2 × 50, is not true for this problem, so we only use Pattern 1 for the missing value.) The missing number is 11. Problem 14: Given: Top-Left = 64, Top-Right = 44, Bottom-Left = 88, Bottom-Right = 42. Missing: Outside Box. Using Pattern 1: Outside Box = 64 + 42 Outside Box = 106 (Note: Pattern 2, 88 = 2 × 44, is true for this problem.) Your answer of 106 is correct. The missing number is 106. Problem 15: Given: Top-Left = 43, Top-Right = 42, Bottom-Left = 84, Outside Box = 62. Missing: Bottom-Right. Using Pattern 1: 43 + Bottom-Right = 62 Bottom-Right = 62 - 43 Bottom-Right = 19 (Note: Pattern 2, 84 = 2 × 42, is true for this problem.) The missing number is 19. Problem 16: Given: Top-Left = 34, Top-Right = 100, Bottom-Left = 11, Outside Box = 45. Missing: Bottom-Right. Using Pattern 1: 34 + Bottom-Right = 45 Bottom-Right = 45 - 34 Bottom-Right = 11 (Note: Pattern 2, 11 = 2 × 100, is not true for this problem, so we only use Pattern 1 for the missing value.) The missing number is 11. Problem 17: Given: Top-Left = 58, Top-Right = 60, Bottom-Left = 120, Bottom-Right = 22. Missing: Outside Box. Using Pattern 1: Outside Box = 58 + 22 Outside Box = 80 (Note: Pattern 2, 120 = 2 × 60, is true for this problem.) Your answer of 80 is correct. The missing number is 80. Problem 18: Given: Top-Left = 73, Bottom-Left = 300, Bottom-Right = 61, Outside Box = 134. Missing: Top-Right. Using Pattern 2: 300 = 2 × Top-Right Top-Right = (300)/(2) Top-Right = 150 (Note: Pattern 1, 73 + 61 = 134, is consistent with the given outside box.) The missing number is 150. Problem 19: Given: Top-Right = 48, Bottom-Left = 96, Bottom-Right = 42, Outside Box = 92. Missing: Top-Left. Using Pattern 1: Top-Left + 42 = 92 Top-Left = 92 - 42 Top-Left = 50 (Note: Pattern 2, 96 = 2 × 48, is true for this problem.) Your answer of 50 is correct. The missing number is 50. Problem 20: Given: Top-Left = 63, Top-Right = 39, Bottom-Left = 78, Outside Box = 80. Missing: Bottom-Right. Using Pattern 1: 63 + Bottom-Right = 80 Bottom-Right = 80 - 63 Bottom-Right = 17 (Note: Pattern 2, 78 = 2 × 39, is true for this problem.) The missing number is 17. Drop the next question!