To solve the problem, we need to determine the values of the shapes (triangle, circle, square, and diamond) based on the given clues. Let's break it down step by step.
Step 1: Define Variables
Let:
- Triangle = \( T \)
- Circle = \( C \)
- Square = \( S \)
- Diamond = \( D \)
Step 2: Translate Clues into Equations
From the clues, we can write the following equations:
1. \( T + T = 6 \)
2. \( C + S = 8 \)
3. \( T + C = 4 \)
4. \( S + D = 10 \)
Step 3: Solve for Each Variable
#### Equation 1: \( T + T = 6 \)
\[ 2T = 6 \]
\[ T = 3 \]
#### Equation 3: \( T + C = 4 \)
Substitute \( T = 3 \):
\[ 3 + C = 4 \]
\[ C = 1 \]
#### Equation 2: \( C + S = 8 \)
Substitute \( C = 1 \):
\[ 1 + S = 8 \]
\[ S = 7 \]
#### Equation 4: \( S + D = 10 \)
Substitute \( S = 7 \):
\[ 7 + D = 10 \]
\[ D = 3 \]
Step 4: Verify the Values
We have:
- \( T = 3 \)
- \( C = 1 \)
- \( S = 7 \)
- \( D = 3 \)
Let's verify these values with the original clues:
1. \( T + T = 3 + 3 = 6 \) (True)
2. \( C + S = 1 + 7 = 8 \) (True)
3. \( T + C = 3 + 1 = 4 \) (True)
4. \( S + D = 7 + 3 = 10 \) (True)
All clues are satisfied, so the values are correct.
Step 5: Solve the Questions
Now, we use the values of \( T \), \( C \), \( S \), and \( D \) to solve the questions on the right side of the image.
#### Question 1: \( T + S + D = ? \)
\[ T + S + D = 3 + 7 + 3 = 13 \]
#### Question 2: \( C + S + T = ? \)
\[ C + S + T = 1 + 7 + 3 = 11 \]
#### Question 3: \( S + S + D = ? \)
\[ S + S + D = 7 + 7 + 3 = 17 \]
#### Question 4: \( T + S + D + C = ? \)
\[ T + S + D + C = 3 + 7 + 3 + 1 = 14 \]
Final Answers
\[
\boxed{13, 11, 17, 14}
\]
Parent Tip: Review the logic above to help your child master the concept of fun math puzzle worksheet for middle school.