Sure! Let’s solve each equation to
find the value of `y`. I’ll go step by step for each problem, explaining the algebraic reasoning.
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🔢 Basic Rule:
To solve for `y`, isolate it on one side of the equation using inverse operations:
- If something is
multiplied by `y`,
divide both sides by that number.
- If something is
added to `y`,
subtract it from both sides.
- If something is
subtracted from `y`,
add it to both sides.
---
##
✔ Solutions:
---
1. 12y = 108
Divide both sides by 12:
→ y = 108 ÷ 12 =
9
---
2. 9y = 54
Divide both sides by 9:
→ y = 54 ÷ 9 =
6
---
3. 11y = 99
Divide both sides by 11:
→ y = 99 ÷ 11 =
9
---
4. 14y = 28
Divide both sides by 14:
→ y = 28 ÷ 14 =
2
---
5. 9y = 45
Divide both sides by 9:
→ y = 45 ÷ 9 =
5
---
6. 7y = 42
Divide both sides by 7:
→ y = 42 ÷ 7 =
6
---
7. 10y = 80
Divide both sides by 10:
→ y = 80 ÷ 10 =
8
---
8. 15y = 45
Divide both sides by 15:
→ y = 45 ÷ 15 =
3
---
9. 6y = 48
Divide both sides by 6:
→ y = 48 ÷ 6 =
8
---
10. 5y = 55
Divide both sides by 5:
→ y = 55 ÷ 5 =
11
---
11. 6y + 15 = 45
Subtract 15 from both sides:
→ 6y = 45 - 15 = 30
Then divide by 6:
→ y = 30 ÷ 6 =
5
---
12. 9y + 15 = 60
Subtract 15 from both sides:
→ 9y = 60 - 15 = 45
Divide by 9:
→ y = 45 ÷ 9 =
5
---
13. 4y + 13 = 33
Subtract 13:
→ 4y = 33 - 13 = 20
Divide by 4:
→ y = 20 ÷ 4 =
5
---
14. 7y + 8 = 50
Subtract 8:
→ 7y = 50 - 8 = 42
Divide by 7:
→ y = 42 ÷ 7 =
6
---
15. 5y + 19 = 79
Subtract 19:
→ 5y = 79 - 19 = 60
Divide by 5:
→ y = 60 ÷ 5 =
12
---
16. 12y - 12 = 48
Add 12 to both sides:
→ 12y = 48 + 12 = 60
Divide by 12:
→ y = 60 ÷ 12 =
5
---
17. 8y - 13 = 27
Add 13:
→ 8y = 27 + 13 = 40
Divide by 8:
→ y = 40 ÷ 8 =
5
---
18. 5y - 10 = 15
Add 10:
→ 5y = 15 + 10 = 25
Divide by 5:
→ y = 25 ÷ 5 =
5
---
19. 3y - 13 = 20
Add 13:
→ 3y = 20 + 13 = 33
Divide by 3:
→ y = 33 ÷ 3 =
11
---
20. 6y - 12 = 60
Add 12:
→ 6y = 60 + 12 = 72
Divide by 6:
→ y = 72 ÷ 6 =
12
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## 📋 Final Answer Key:
| Problem | Value of y |
|---------|------------|
| 1 | 9 |
| 2 | 6 |
| 3 | 9 |
| 4 | 2 |
| 5 | 5 |
| 6 | 6 |
| 7 | 8 |
| 8 | 3 |
| 9 | 8 |
| 10 | 11 |
| 11 | 5 |
| 12 | 5 |
| 13 | 5 |
| 14 | 6 |
| 15 | 12 |
| 16 | 5 |
| 17 | 5 |
| 18 | 5 |
| 19 | 11 |
| 20 | 12 |
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✔ All problems solved using basic algebra: isolate `y` by reversing operations (add/subtract first, then multiply/divide).
Let me know if you’d like a printable version or want to check your work!
Parent Tip: Review the logic above to help your child master the concept of basic algebra worksheet and answers.
