jakes numbered the houses on a straight road from 80 to 180 using different digits. how many 4's and 8's did jakes use?

To solve the problem, we'll break down the numbers on the road and count how many times the digits 4 and 8 appear.

Jake numbered the houses from 80 to 180, inclusive. So, let's consider the range from 80 to 180.

### Counting the Digit '4':
- **In the tens place:**
  - The digit 4 will appear in the tens place in numbers from 140 to 149.
  - So, it appears 10 times (140, 141, 142, 143, 144, 145, 146, 147, 148, 149).
  
- **In the units place:**
  - The digit 4 appears in the units place in numbers like 84, 94, 104, 114, 124, 134, 144, 154, 164, 174.
  - This gives us 10 occurrences.

- **In the hundreds place:**
  - For the given range (80 to 180), the digit 4 does not appear in the hundreds place.

So, the digit 4 appears a total of \(10 + 10 = 20\) times.

### Counting the Digit '8':
- **In the tens place:**
  - The digit 8 will appear in the tens place in numbers from 80 to 89.
  - So, it appears 10 times (80, 81, 82, 83, 84, 85, 86, 87, 88, 89).
  
- **In the units place:**
  - The digit 8 appears in the units place in numbers like 88, 98, 108, 118, 128, 138, 148, 158, 168, 178.
  - This gives us 10 occurrences.

- **In the hundreds place:**
  - For the given range (80 to 180), the digit 8 does not appear in the hundreds place.

So, the digit 8 appears a total of \(10 + 10 = 20\) times.

### Final Answer:
- The digit 4 is used **20** times.
- The digit 8 is used **20** times.

Would you like more details or have any questions?

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Here are 8 related questions you might find interesting:
1. How many times does the digit 1 appear between 80 and 180?
2. How many numbers between 80 and 180 contain the digit 0?
3. What is the total sum of the digits in all the numbers between 80 and 180?
4. How many numbers between 100 and 200 contain the digit 5?
5. If the numbering had started from 70 instead of 80, how would the count of digit 7 differ?
6. How many times does the digit 9 appear in the range 90 to 190?
7. What is the largest prime number between 80 and 180?
8. How many palindromic numbers are there between 80 and 180?

**Tip:** When counting the occurrence of a digit in a range, it's useful to break down the problem by place value (units, tens, hundreds).

Learn how many times the digits 4 and 8 appear in the numbering of houses from 80 to 180. This problem involves counting occurrences based on place value (units and tens) within a specified range. Suitable for students in Grades 3-5.

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