Mrs. Rossi wrote the following clues for a mystery number. It is a 4-digit number. The tens are double the ones. The thousands are double the tens. The sum of the digits is 19.

Question

Mrs. Rossi wrote the following clues for a mystery number. It is a 4-digit number. The tens are double the ones. The thousands are double the tens. The sum of the digits is 19.

Answer 1

let the hundreds be X

so the only possible cases are

4X21 and 8X42

to have a sum of 19 X can only be 5

(it would have to be 12 for the first case, not possible)

The number is 8542

Answer 2

4321

1234
1533
1234567890

Answer 3

Mrs rossi wrote the following clue first a mystery number

It is a 3-digit number the tens are double the ones the hundreds are double the tens
The sum of the digital is 14 what is the number

Answer 4

To find the mystery number, let's analyze the clues one by one.

1. "The tens are double the ones."
Let's represent the ones digit as "x." Since the tens digit is double the ones digit, we can express it as 2x.

2. "The thousands are double the tens."
Similarly, the thousands digit is double the tens digit. So, we'll represent the tens digit as "y," and the thousands digit would be 2y.

3. "The sum of the digits is 19."
This clue means that the sum of the thousands digit (2y), the hundreds digit (let's call it "z"), the tens digit (2x), and the ones digit (x) is 19. So, we can write the equation as:
2y + z + 2x + x = 19

Now, we need to solve this system of equations to find the values of x, y, and z.

Let's put the equations together:

2y + z + 2x + x = 19

From here, we can simplify the equation:

3x + 3y + z = 19

Now we can look for possible values of x, y, and z that satisfy the equation.

Since we're dealing with a 4-digit number, all the digits must be between 0 and 9.

We'll use a trial and error method to find the values that satisfy the equation.

Let's start with x = 1, y = 2, and z = 4:

3(1) + 3(2) + 4 = 3 + 6 + 4 = 13 (not equal to 19)

Let's try another set of values:

x = 3, y = 6, and z = 3:

3(3) + 3(6) + 3 = 9 + 18 + 3 = 30 (not equal to 19)

Continuing in this way, we can try different combinations of x, y, and z until we find a set of values that satisfies the equation.

After some trial and error, we find that when x = 2, y = 4, and z = 1, the equation is satisfied:

3(2) + 3(4) + 1 = 6 + 12 + 1 = 19

Therefore, the mystery number is 2416.