Let’s solve this step by step.
We are given 5 equations with shapes representing unknown numbers:
1. ○ + △ = 8
2. ○ - △ = 4
3. ★ + □ = 12
4. ★ - □ = □
5. □ + □ = ★
We need to find the values of ★, ○, □, and △.
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Step 1: Solve for ○ and △ using equations (1) and (2)
Equation (1): ○ + △ = 8
Equation (2): ○ - △ = 4
Add these two equations together:
(○ + △) + (○ - △) = 8 + 4
→ ○ + △ + ○ - △ = 12
→ 2○ = 12
→ ○ =
6
Now plug ○ = 6 into equation (1):
6 + △ = 8 → △ =
2
✔ So far:
○ = 6
△ = 2
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Step 2: Solve for ★ and □ using equations (3), (4), and (5)
We have:
Equation (3): ★ + □ = 12
Equation (4): ★ - □ = □
Equation (5): □ + □ = ★ → which is ★ = 2□
Let’s use equation (5) to substitute into equation (3).
From (5): ★ = 2□
Plug into (3):
2□ + □ = 12 → 3□ = 12 → □ =
4
Then from (5): ★ = 2 × 4 =
8
✔ So:
□ = 4
★ = 8
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Step 3: Verify with equation (4)
Equation (4): ★ - □ = □
Left side: 8 - 4 = 4
Right side: □ = 4
→ 4 = 4
✔ Correct!
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Final Answer:
⭐ Star (★) =
8
⭕ Circle (○) =
6
⬜ Square (□) =
4
🔺 Triangle (△) =
2
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Bonus: Fill in the blanks as shown in the image:
- ★ =
8
- ○ =
6
- □ =
4
- △ =
2
Also, the incomplete equations:
- ★ - □ = □ → 8 - 4 = 4
✔
- □ + □ = ★ → 4 + 4 = 8
✔
All equations check out!
✔ Final Values:
- ★ = 8
- ○ = 6
- □ = 4
- △ = 2
Parent Tip: Review the logic above to help your child master the concept of math brain teasers worksheet.
