To solve the problem, we need to determine the values of the yellow squares in the grid. Let's denote the yellow squares as follows:
- Top-left square: \( A \)
- Top-right square: \( B \)
- Bottom-left square: \( C \)
- Bottom-right square: \( D \)
The grid provides us with the following equations:
1. \( A + B = 8 \)
2. \( C - D = 6 \)
3. \( A + C = 13 \)
4. \( B + D = 8 \)
We will solve these equations step by step.
Step 1: Solve for \( A \) and \( B \) using \( A + B = 8 \)
From equation (1):
\[ A + B = 8 \]
Step 2: Solve for \( C \) and \( D \) using \( C - D = 6 \)
From equation (2):
\[ C - D = 6 \]
Step 3: Use \( A + C = 13 \) to express \( C \) in terms of \( A \)
From equation (3):
\[ A + C = 13 \]
\[ C = 13 - A \]
Step 4: Use \( B + D = 8 \) to express \( D \) in terms of \( B \)
From equation (4):
\[ B + D = 8 \]
\[ D = 8 - B \]
Step 5: Substitute \( C \) and \( D \) into \( C - D = 6 \)
Substitute \( C = 13 - A \) and \( D = 8 - B \) into equation (2):
\[ C - D = 6 \]
\[ (13 - A) - (8 - B) = 6 \]
\[ 13 - A - 8 + B = 6 \]
\[ 5 - A + B = 6 \]
\[ -A + B = 1 \]
\[ B = A + 1 \]
Step 6: Substitute \( B = A + 1 \) into \( A + B = 8 \)
Substitute \( B = A + 1 \) into equation (1):
\[ A + B = 8 \]
\[ A + (A + 1) = 8 \]
\[ 2A + 1 = 8 \]
\[ 2A = 7 \]
\[ A = 5 \]
Step 7: Find \( B \)
Using \( B = A + 1 \):
\[ B = 5 + 1 \]
\[ B = 6 \]
Step 8: Find \( C \)
Using \( C = 13 - A \):
\[ C = 13 - 5 \]
\[ C = 8 \]
Step 9: Find \( D \)
Using \( D = 8 - B \):
\[ D = 8 - 6 \]
\[ D = 2 \]
Final Answer
The values of the yellow squares are:
- \( A = 5 \)
- \( B = 6 \)
- \( C = 8 \)
- \( D = 2 \)
Thus, the solution is:
\[
\boxed{5, 6, 8, 2}
\]
Parent Tip: Review the logic above to help your child master the concept of math puzzles.
