what three digit number is less than 300 and the ones digit is 4 times the hundreds digit and the tens digit is 5 more than the hundreds digit and the sum of the digits is 17

(1-2i)(1+2i)

278

To find the three-digit number that satisfies all the given conditions, we need to break down the problem into smaller steps and find the answer systematically.

Let's assume the digits of the three-digit number are represented as follows: ABC, where A represents the hundreds digit, B represents the tens digit, and C represents the ones digit.

From the given conditions, we can deduce the following equations:

1. The number is less than 300: A < 3.
2. The ones digit is 4 times the hundreds digit: C = 4A.
3. The tens digit is 5 more than the hundreds digit: B = A + 5.
4. The sum of the digits is 17: A + B + C = 17.

Let's substitute the values we have derived from the conditions into the equation we found in step 4:

A + B + C = 17
A + (A + 5) + 4A = 17
6A + 5 = 17
6A = 12
A = 2

Now that we have found the value of A, we can substitute it back into equations 2 and 3 to find the values of B and C:

From equation 2: C = 4A = 4 * 2 = 8
From equation 3: B = A + 5 = 2 + 5 = 7

Therefore, the three-digit number that satisfies all the given conditions is 278.