I'll solve each algebra problem step by step, finding the value of y for all 20 equations.
Let me work through each one carefully:
Problems 1-10 (Simple multiplication):
1. 3y = 27
- Divide both sides by 3: y = 27 ÷ 3 = 9
2. 9y = 81
- Divide both sides by 9: y = 81 ÷ 9 = 9
3. 12y = 132
- Divide both sides by 12: y = 132 ÷ 12 = 11
4. 6y = 72
- Divide both sides by 6: y = 72 ÷ 6 = 12
5. 20y = 120
- Divide both sides by 20: y = 120 ÷ 20 = 6
6. 15y = 75
- Divide both sides by 15: y = 75 ÷ 15 = 5
7. 10y = 160
- Divide both sides by 10: y = 160 ÷ 10 = 16
8. 9y = 72
- Divide both sides by 9: y = 72 ÷ 9 = 8
9. 11y = 88
- Divide both sides by 11: y = 88 ÷ 11 = 8
10. 4y = 36
- Divide both sides by 4: y = 36 ÷ 4 = 9
Problems 11-20 (With addition/subtraction):
11. 5y + 15 = 65
- Subtract 15 from both sides: 5y = 50
- Divide by 5: y = 10
12. 9y + 20 = 83
- Subtract 20 from both sides: 9y = 63
- Divide by 9: y = 7
13. 7y + 9 = 44
- Subtract 9 from both sides: 7y = 35
- Divide by 7: y = 5
14. 4y + 18 = 34
- Subtract 18 from both sides: 4y = 16
- Divide by 4: y = 4
15. 6y + 40 = 100
- Subtract 40 from both sides: 6y = 60
- Divide by 6: y = 10
16. 12y - 15 = 45
- Add 15 to both sides: 12y = 60
- Divide by 12: y = 5
17. 8y - 22 = 42
- Add 22 to both sides: 8y = 64
- Divide by 8: y = 8
18. 5y - 8 = 27
- Add 8 to both sides: 5y = 35
- Divide by 5: y = 7
19. 11y - 13 = 53
- Add 13 to both sides: 11y = 66
- Divide by 11: y = 6
20. 3y - 24 = 0
- Add 24 to both sides: 3y = 24
- Divide by 3: y = 8
Let me verify a few calculations to make sure they're correct:
- #3: 12 × 11 = 132 ✓
- #5: 20 × 6 = 120 ✓
- #11: 5(10) + 15 = 50 + 15 = 65 ✓
- #17: 8(8) - 22 = 64 - 22 = 42 ✓
- #20: 3(8) - 24 = 24 - 24 = 0 ✓
Final Answer:
1. y = 9
2. y = 9
3. y = 11
4. y = 12
5. y = 6
6. y = 5
7. y = 16
8. y = 8
9. y = 8
10. y = 9
11. y = 10
12. y = 7
13. y = 5
14. y = 4
15. y = 10
16. y = 5
17. y = 8
18. y = 7
19. y = 6
20. y = 8
Parent Tip: Review the logic above to help your child master the concept of fifth grade algebra worksheet.
