To solve this puzzle, we need to determine the value of each food item (hamburger, pizza slice, ice cream cone, and donut) using the given equations. Let's break it down step by step.
Step 1: Assign Variables
Let:
- \( H \) = Value of the hamburger
- \( P \) = Value of the pizza slice
- \( I \) = Value of the ice cream cone
- \( D \) = Value of the donut
Step 2: Translate the Equations
The given equations are:
1. \( H + P = I + 1 \)
2. \( D + H + D = P \)
3. \( D \times I = 0 \)
4. \( I - 3 = 2 \)
5. \( H \times P + I = ? \)
Step 3: Solve Each Equation
#### Equation 4: \( I - 3 = 2 \)
\[ I - 3 = 2 \]
\[ I = 2 + 3 \]
\[ I = 5 \]
So, the value of the ice cream cone (\( I \)) is 5.
#### Equation 3: \( D \times I = 0 \)
Since \( I = 5 \):
\[ D \times 5 = 0 \]
\[ D = 0 \]
So, the value of the donut (\( D \)) is 0.
#### Equation 2: \( D + H + D = P \)
Substitute \( D = 0 \):
\[ 0 + H + 0 = P \]
\[ H = P \]
So, the value of the hamburger (\( H \)) is equal to the value of the pizza slice (\( P \)).
#### Equation 1: \( H + P = I + 1 \)
Substitute \( I = 5 \) and \( H = P \):
\[ H + H = 5 + 1 \]
\[ 2H = 6 \]
\[ H = 3 \]
Since \( H = P \):
\[ P = 3 \]
Step 4: Verify the Values
We have:
- \( H = 3 \)
- \( P = 3 \)
- \( I = 5 \)
- \( D = 0 \)
Let's verify these values with the original equations:
1. \( H + P = I + 1 \)
\[ 3 + 3 = 5 + 1 \]
\[ 6 = 6 \] (True)
2. \( D + H + D = P \)
\[ 0 + 3 + 0 = 3 \]
\[ 3 = 3 \] (True)
3. \( D \times I = 0 \)
\[ 0 \times 5 = 0 \]
\[ 0 = 0 \] (True)
4. \( I - 3 = 2 \)
\[ 5 - 3 = 2 \]
\[ 2 = 2 \] (True)
All equations are satisfied.
Step 5: Solve the Final Equation
The final equation is:
\[ H \times P + I = ? \]
Substitute the values:
\[ H = 3, \, P = 3, \, I = 5 \]
\[ 3 \times 3 + 5 = ? \]
\[ 9 + 5 = ? \]
\[ ? = 14 \]
Final Answer:
\[
\boxed{14}
\]
Parent Tip: Review the logic above to help your child master the concept of math coloring worksheet 5th grade.
