There are eight houses on Jerry's side of the street. All the house numbers are even numbers from 2 to 16 . Jerry noticed that the sum of the house numbers to the left of his house equals the sum of the house numbers to the right of his house. What is the number of Jerry's house?
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Let’s analyze the house numbers on Jerry's side of the street, which are 2, 4, 6, 8, 10, 12, 14, and 16. The total sum of these house numbers is: \[ 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 = 72 \] If Jerry lives in the house numbered \( x \), the sum of the house numbers to the left of his house and to the right should be equal. This means that the sum of the left side equals: \[ \frac{72 - x}{2} \] To find Jerry's house number, we can check each house number (excluding 2 and 16, as those can't split the houses into two sides): - If \( x = 6 \): Left: 2 + 4 = 6, Right: 8 + 10 + 12 + 14 + 16 = 60 (not equal) - If \( x = 8 \): Left: 2 + 4 + 6 = 12, Right: 10 + 12 + 14 + 16 = 52 (not equal) - If \( x = 10 \): Left: 2 + 4 + 6 + 8 = 20, Right: 12 + 14 + 16 = 42 (not equal) - If \( x = 12 \): Left: 2 + 4 + 6 + 8 + 10 = 30, Right: 14 + 16 = 30 (equal) So, Jerry's house number is **12**.
