The Best Free 7th Grade Math Resources: Complete List! — Mashup Math - Free Printable

The image contains three math puzzles. Let's solve each one step by step.

---

Puzzle 1: Color Grid Problem

Problem Statement:
"If the diagram below represents 250, find the value of each color."

The grid is divided into different colored sections:
- Green
- Blue
- Yellow
- Pink

#### Solution:
1. Count the total number of squares in the grid:
- The grid appears to be a 10x10 grid, which means there are \(10 \times 10 = 100\) squares in total.

2. Determine the value per square:
- The entire grid represents 250.
- Since there are 100 squares, the value of each square is:
\[
\frac{250}{100} = 2.5
\]

3. Calculate the value of each colored section:
- Green: There are 40 green squares.
\[
40 \times 2.5 = 100
\]
- Blue: There are 30 blue squares.
\[
30 \times 2.5 = 75
\]
- Yellow: There are 20 yellow squares.
\[
20 \times 2.5 = 50
\]
- Pink: There are 10 pink squares.
\[
10 \times 2.5 = 25
\]

#### Final Answer for Puzzle 1:
\[
\boxed{\text{Green: 100, Blue: 75, Yellow: 50, Pink: 25}}
\]

---

Puzzle 2: Symbol Arithmetic Problem

Problem Statement:
Solve the following equations involving symbols:
1. 🍦 × 🍪 = 36
2. 🍦 + 🍪 = 36
3. 🍦 ÷ 🍪 = 20
4. ? = ?

#### Solution:
Let:
- 🍦 = \( x \)
- 🍪 = \( y \)

From the equations:
1. \( x \times y = 36 \)
2. \( x + y = 36 \)
3. \( x \div y = 20 \)

#### Step 1: Solve for \( x \) and \( y \) using the first two equations.
From \( x \times y = 36 \):
\[
y = \frac{36}{x}
\]

Substitute \( y = \frac{36}{x} \) into \( x + y = 36 \):
\[
x + \frac{36}{x} = 36
\]

Multiply through by \( x \) to clear the fraction:
\[
x^2 + 36 = 36x
\]

Rearrange into standard quadratic form:
\[
x^2 - 36x + 36 = 0
\]

Solve this quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -36 \), and \( c = 36 \):
\[
x = \frac{36 \pm \sqrt{(-36)^2 - 4 \cdot 1 \cdot 36}}{2 \cdot 1}
\]
\[
x = \frac{36 \pm \sqrt{1296 - 144}}{2}
\]
\[
x = \frac{36 \pm \sqrt{1152}}{2}
\]
\[
x = \frac{36 \pm 24\sqrt{2}}{2}
\]
\[
x = 18 \pm 12\sqrt{2}
\]

Since \( x \) and \( y \) must be positive integers (as they represent quantities), we need to re-evaluate the problem. The third equation \( x \div y = 20 \) suggests a simpler approach.

#### Step 2: Use the third equation \( x \div y = 20 \).
\[
x = 20y
\]

Substitute \( x = 20y \) into \( x \times y = 36 \):
\[
(20y) \times y = 36
\]
\[
20y^2 = 36
\]
\[
y^2 = \frac{36}{20}
\]
\[
y^2 = 1.8
\]

This does not yield integer solutions, so let's recheck the problem setup. The third equation might be misinterpreted. Instead, let's assume the symbols represent specific values that satisfy all equations simultaneously.

#### Correct Approach:
Given the complexity, let's assume the symbols represent specific values that satisfy the equations. By trial and error or logical deduction:
- If \( x = 36 \) and \( y = 1 \):
- \( x \times y = 36 \times 1 = 36 \) (satisfied)
- \( x + y = 36 + 1 = 37 \) (not satisfied)

Re-evaluate the problem constraints or assumptions. The correct interpretation might involve rechecking the problem statement or additional context.

#### Final Answer for Puzzle 2:
\[
\boxed{\text{Insufficient information for exact solution without clarification}}
\]

---

Puzzle 3: Hexagonal Pattern Problem

Problem Statement:
"Look for a pattern to find the value of the ? in the diagram below."

The hexagonal pattern is as follows:
```
1
1 1
1 2 1
1 3 3 1
1 4 ? 4 1
```

#### Solution:
1. Identify the pattern:
- The numbers in the hexagons follow a specific rule. Observing the pattern:
- The outermost layer has 1s.
- The second layer has 1, 2, 1.
- The third layer has 1, 3, 3, 1.
- The fourth layer has 1, 4, ?, 4, 1.

2. Determine the rule:
- Each number in the hexagon is the sum of the two numbers directly above it in the previous layer.
- For example:
- In the third layer: \( 2 = 1 + 1 \)
- In the fourth layer: \( 3 = 1 + 2 \) and \( 3 = 2 + 1 \)

3. Apply the rule to find the missing value (?):
- The missing value (?) is the sum of the two numbers directly above it in the third layer:
\[
? = 3 + 3 = 6
\]

#### Final Answer for Puzzle 3:
\[
\boxed{6}
\]

---

Summary of Answers:

1. Color Grid Problem: Green: 100, Blue: 75, Yellow: 50, Pink: 25
2. Symbol Arithmetic Problem: Insufficient information for exact solution without clarification
3. Hexagonal Pattern Problem: 6

\[
\boxed{6}
\]