Pregunta
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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?

Ask by Osborne Parsons. in South Africa
Mar 10,2025

Solución de inteligencia artificial de Upstudy

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Jerry’s house number is 12.

Solución

Step 1. List the House Numbers
The houses have even numbers from 2 to 16:
Step 2. Calculate the Total Sum
The total sum of all houses is:
We can calculate by pairing or using the formula for an arithmetic series. Notice there are 8 terms, with the first term and the last term :
Step 3. Set Up the Equation
Let Jerry’s house be numbered . The houses to the left of Jerry’s house will have a sum and the houses to the right of Jerry’s house will have a sum . According to the problem:
Also, since is not included in either sum:
Substitute :
Step 4. Find the Correct House Number
must be the sum of all house numbers smaller than among the given list. We check the house numbers one by one:
  • For :
    Instead, using the formula:
    .
  • For :
    Formula gives:
  • For :
    Formula gives:
  • For :
    Formula gives:
  • For :
    Formula gives:
  • For :
    Formula gives:
    Here, the two values match.
Step 5. Conclusion
Since for the condition holds true, Jerry’s house is numbered:

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The Deep Dive

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:
If Jerry lives in the house numbered , 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:
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 :
    Left: 2 + 4 = 6, Right: 8 + 10 + 12 + 14 + 16 = 60 (not equal)
  • If :
    Left: 2 + 4 + 6 = 12, Right: 10 + 12 + 14 + 16 = 52 (not equal)
  • If :
    Left: 2 + 4 + 6 + 8 = 20, Right: 12 + 14 + 16 = 42 (not equal)
  • If :
    Left: 2 + 4 + 6 + 8 + 10 = 30, Right: 14 + 16 = 30 (equal)
So, Jerry’s house number is 12.

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