Puzzle Time!
#### Directions: Find the value of each symbol and the "?".
We are given the following equations with symbols representing numbers. Let's solve step by step.
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#### Symbols:
1. Smartphone: \( S \)
2. Game Console: \( G \)
3. Controller: \( C \)
4. Handheld Game Device: \( H \)
#### Equations:
1. \( S + G + C = 23 \)
2. \( S = C \)
3. \( H - G = 13 \)
4. \( G + H = 27 \)
5. \( S + G + C + H = ? \)
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Step 1: Use Equation 2 (\( S = C \))
From Equation 2, we know:
\[ S = C \]
Substitute \( C \) with \( S \) in Equation 1:
\[ S + G + S = 23 \]
\[ 2S + G = 23 \quad \text{(Equation 1')} \]
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Step 2: Solve for \( G \) and \( H \) using Equations 3 and 4
From Equation 3:
\[ H - G = 13 \quad \text{(Equation 3)} \]
From Equation 4:
\[ G + H = 27 \quad \text{(Equation 4)} \]
Add Equations 3 and 4:
\[ (H - G) + (G + H) = 13 + 27 \]
\[ 2H = 40 \]
\[ H = 20 \]
Substitute \( H = 20 \) into Equation 3:
\[ 20 - G = 13 \]
\[ G = 7 \]
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Step 3: Solve for \( S \) using Equation 1'
From Equation 1':
\[ 2S + G = 23 \]
Substitute \( G = 7 \):
\[ 2S + 7 = 23 \]
\[ 2S = 16 \]
\[ S = 8 \]
Since \( S = C \), we also have:
\[ C = 8 \]
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Step 4: Verify all values
We have:
- \( S = 8 \)
- \( G = 7 \)
- \( C = 8 \)
- \( H = 20 \)
Verify Equation 1:
\[ S + G + C = 8 + 7 + 8 = 23 \] (Correct)
Verify Equation 3:
\[ H - G = 20 - 7 = 13 \] (Correct)
Verify Equation 4:
\[ G + H = 7 + 20 = 27 \] (Correct)
All values are consistent.
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Step 5: Solve for the "?"
The final equation is:
\[ S + G + C + H = ? \]
Substitute the values:
\[ 8 + 7 + 8 + 20 = 43 \]
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Final Answer:
\[
\boxed{43}
\]
Parent Tip: Review the logic above to help your child master the concept of 6th grade math puzzles worksheet.
