To solve these equations, I need to find the value of each letter by subtracting the known number from the total. Let me work through each equation carefully:
Column 1:
1. k + 7 = 10 → k = 10 - 7 =
3
2. 5 + m = 8 → m = 8 - 5 =
3
3. d + 1 = 3 → d = 3 - 1 =
2
4. 5 + y = 8 → y = 8 - 5 =
3
5. 8 + c = 11 → c = 11 - 8 =
3
6. 8 + x = 9 → x = 9 - 8 =
1
7. 8 + u = 17 → u = 17 - 8 =
9
8. 1 + d = 9 → d = 9 - 1 =
8
9. 2 + j = 7 → j = 7 - 2 =
5
10. 1 + q = 8 → q = 8 - 1 =
7
Column 2:
11. 2 + s = 9 → s = 9 - 2 =
7
12. 2 + s = 10 → s = 10 - 2 =
8
13. 8 + z = 9 → z = 9 - 8 =
1
14. g + 6 = 9 → g = 9 - 6 =
3
15. 6 + n = 12 → n = 12 - 6 =
6
16. s + 4 = 13 → s = 13 - 4 =
9
17. 5 + t = 11 → t = 11 - 5 =
6
18. 2 + u = 10 → u = 10 - 2 =
8
19. c + 5 = 12 → c = 12 - 5 =
7
20. 9 + q = 14 → q = 14 - 9 =
5
Column 3:
21. 7 + q = 12 → q = 12 - 7 =
5
22. 3 + d = 9 → d = 9 - 3 =
6
23. 8 + n = 17 → n = 17 - 8 =
9
24. 1 + s = 10 → s = 10 - 1 =
9
25. v + 8 = 15 → v = 15 - 8 =
7
26. b + 7 = 16 → b = 16 - 7 =
9
27. r + 4 = 8 → r = 8 - 4 =
4
28. k + 7 = 10 → k = 10 - 7 =
3
29. g + 9 = 15 → g = 15 - 9 =
6
30. 7 + n = 14 → n = 14 - 7 =
7
Column 4:
31. 7 + r = 13 → r = 13 - 7 =
6
32. 3 + x = 9 → x = 9 - 3 =
6
33. c + 5 = 7 → c = 7 - 5 =
2
34. z + 3 = 5 → z = 5 - 3 =
2
35. t + 7 = 10 → t = 10 - 7 =
3
36. 2 + s = 11 → s = 11 - 2 =
9
37. 9 + c = 16 → c = 16 - 9 =
7
38. 5 + s = 8 → s = 8 - 5 =
3
39. 5 + c = 8 → c = 8 - 5 =
3
40. u + 2 = 10 → u = 10 - 2 =
8
Let me verify a few key calculations:
- k + 7 = 10: k = 3 ✓ (3 + 7 = 10)
- 8 + u = 17: u = 9 ✓ (8 + 9 = 17)
- 1 + d = 9: d = 8 ✓ (1 + 8 = 9)
- s + 4 = 13: s = 9 ✓ (9 + 4 = 13)
- v + 8 = 15: v = 7 ✓ (7 + 8 = 15)
- b + 7 = 16: b = 9 ✓ (9 + 7 = 16)
- 9 + q = 14: q = 5 ✓ (9 + 5 = 14)
- 7 + n = 14: n = 7 ✓ (7 + 7 = 14)
All calculations check out. Now I'll present the final answer in an organized format.
Final Answer:
k = 3, m = 3, d = 2 (row 3), y = 3, c = 3 (row 5), x = 1, u = 9, d = 8 (row 8), j = 5, q = 7
s = 7 (row 1 col 2), s = 8 (row 2 col 2), z = 1, g = 3, n = 6, s = 9 (row 6 col 2), t = 6, u = 8, c = 7 (row 9 col 2), q = 5 (row 10 col 2)
q = 5 (row 1 col 3), d = 6, n = 9, s = 9 (row 4 col 3), v = 7, b = 9, r = 4, k = 3, g = 6, n = 7
r = 6, x = 6, c = 2 (row 3 col 4), z = 2, t = 3, s = 9 (row 6 col 4), c = 7 (row 7 col 4), s = 3, c = 3, u = 8
Note: Some variables appear multiple times with different values because they represent different instances in different equations (e.g., 'd' appears as both 2 and 8, 'c' appears as 3, 7, 2, and 3). Each equation is solved independently.
Parent Tip: Review the logic above to help your child master the concept of missing numbers in equations worksheet.