COMMON CORE MATH LOGIC PUZZLES: SYMBOL MATH PUZZLES TO IMPROVE IQ ... - Free Printable

Let's solve this symbol math logic puzzle step by step.

We are given a series of equations using colored shapes:

- Red circle (🔴)
- Green diamond (🟢)
- Purple triangle (🟣)
- Blue square (🔵)

Each shape represents a number. Our goal is to determine the value of each shape and then find the total for the final row.

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Step 1: Assign Variables

Let:
- 🔴 = R
- 🟢 = G
- 🟣 = T
- 🔵 = S

Now write equations based on the rows:

1. 🔴 + 🔴 + 🟢 + 🟢 = 32
→ 2R + 2G = 32
→ R + G = 16 → (Equation A)

2. 🔴 + 🔴 + 🟣 + 🟣 = 24
→ 2R + 2T = 24
→ R + T = 12 → (Equation B)

3. 🔴 + 🔴 + 🔵 + 🔵 = 42
→ 2R + 2S = 42
→ R + S = 21 → (Equation C)

4. 🟣 + 🟣 + 🔵 + 🔵 = 22
→ 2T + 2S = 22
→ T + S = 11 → (Equation D)

5. 🟢 + 🟢 + 🔵 + 🟣 = 21
→ 2G + S + T = 21 → (Equation E)

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Step 2: Solve the system of equations

From Equation A:
R + G = 16 → G = 16 - R

From Equation B:
R + T = 12 → T = 12 - R

From Equation C:
R + S = 21 → S = 21 - R

From Equation D:
T + S = 11

Substitute T and S from above into Equation D:

(12 - R) + (21 - R) = 11
33 - 2R = 11
2R = 22
→ R = 11

Now substitute back:

- G = 16 - R = 16 - 11 = 5
- T = 12 - R = 12 - 11 = 1
- S = 21 - R = 21 - 11 = 10

Check with Equation E:
2G + S + T = 2(5) + 10 + 1 = 10 + 10 + 1 = 21 ✔

Perfect! All values match.

So:
- 🔴 (Red circle) = 11
- 🟢 (Green diamond) = 5
- 🟣 (Purple triangle) = 1
- 🔵 (Blue square) = 10

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Step 3: Evaluate the Final Row

The bottom row has:
- 🔵, 🔴, 🟢, 🟣

So:
= S + R + G + T
= 10 + 11 + 5 + 1 = 27

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✔ Final Answer: 27

This is the value of the last row.

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Summary:

| Shape | Value |
|--------------|-------|
| 🔴 (Red Circle) | 11 |
| 🟢 (Green Diamond) | 5 |
| 🟣 (Purple Triangle) | 1 |
| 🔵 (Blue Square) | 10 |

Final sum: 10 + 11 + 5 + 1 = 27

✔ Answer: 27