My thousands digit is 2 more than my ones. My tens place is 2 less than the sum of my ones and thousands digits. My hundreds digit is the difference of my ones and thousands digit. What number am I
Answer (1)
Answer:Let's break down the clues and use algebra to solve the problem:1. **Thousands digit is 2 more than my ones digit**: - Let the ones digit be x. - The thousands digit would then be x + 2.2. **Tens place is 2 less than the sum of my ones and thousands digits**: - The sum of the ones and thousands digits is x + (x + 2) = 2x + 2. - The tens digit is 2 less than that sum: (2x + 2) - 2 = 2x.3. **Hundreds digit is the difference between my ones and thousands digits**: - The difference between the ones and thousands digits is (x + 2) - x = 2. - So, the hundreds digit is 2.Now, we have the following:- Ones digit: x- Thousands digit: x + 2- Hundreds digit: 2- Tens digit: 2xThe number is in the form (thousands digit)(hundreds digit)(tens digit)(ones digit), so the number is (x + 2) 2 (2x) x.Let's check if x = 1 works:- Thousands digit: 1 + 2 = 3- Hundreds digit: 2 (given)- Tens digit: 2(1) = 2- Ones digit: 1Thus, the number is 3, 2, 2, 1, or **3221**.Let’s verify:- The thousands digit (3) is 2 more than the ones digit (1). ✅- The tens digit (2) is 2 less than the sum of the ones (1) and thousands (3) digits. The sum is 1 + 3 = 4, and 4 - 2 = 2. ✅- The hundreds digit (2) is the difference between the ones (1) and thousands (3) digits. 3 - 1 = 2. ✅So the number is **3221**.
