Let’s solve the puzzle by assigning variables to the smiley faces:
- Let the happy face (😊) be xxx.
- Let the sad face (☹️) be yyy.
The puzzle gives us three equations:
- x+y=13x + y = 13x+y=13
- x×y=42x \times y = 42x×y=42
- x−y=1x – y = 1x−y=1
We need to solve these equations to find the values of xxx and yyy.
Step 1: Solve the first and third equations
From the third equation: x−y=1x – y = 1x−y=1 x=y+1x = y + 1x=y+1
Step 2: Substitute x=y+1x = y + 1x=y+1 into the first equation
Substituting into the first equation: (y+1)+y=13(y + 1) + y = 13(y+1)+y=13 2y+1=132y + 1 = 132y+1=13 2y=122y = 122y=12 y=6y = 6y=6
Step 3: Find the value of xxx
Substitute y=6y = 6y=6 back into the equation x=y+1x = y + 1x=y+1: x=6+1=7x = 6 + 1 = 7x=6+1=7
Step 4: Verify using the second equation
Substitute x=7x = 7x=7 and y=6y = 6y=6 into the second equation: x×y=7×6=42x \times y = 7 \times 6 = 42x×y=7×6=42
This matches the equation, so the solution is correct.
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Final Answer:
The sad face (☹️) represents y=6y = 6y=6.
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