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.
What number is it?
ones digit --- x
tens digit ---- 2x
thousands --- 4x
hundreds -----y
x+2x + 4x + y = 19
y = 19-7x
but x and y must be single digit positive integers.
let x = 1, then y = 12 , not possible
let x = 2, then y = 5
The number is 8542
let x = 3, then y = 19-21 = negative, no good
any higher number of x will make things even worse
so the number is 8542
Let's break down the information given:
1. The tens are double the ones.
Let's represent the ones digit as x, so the tens digit will be 2x.
2. The thousands are double the tens.
Since the thousands digit is double the tens digit, it will be 2 * (2x), which is 4x.
3. The sum of the digits is 19.
The sum of all digits will be x + 2x + 4x = 7x, and we know this equals 19. So, 7x = 19.
Now, let's solve for x to find the value of the ones digit:
7x = 19
Divide both sides by 7:
x = 19/7
x ≈ 2.71
Since we are dealing with a 4-digit number, x cannot be a decimal value. So, we round x to the nearest whole number, which is 3.
Now that we know x = 3, we can find the other digits:
The ones digit is 3.
The tens digit is double the ones, so it is 2 * 3 = 6.
The thousands digit is double the tens, so it is 2 * 6 = 12.
Therefore, the number is 1236.
To find the number described, we can use a systematic approach and break down each piece of information provided.
First, let's analyze the statement "The tens are double the ones." This means that the tens digit is twice the value of the ones digit. Let's represent the ones digit as "x." Therefore, the tens digit would be "2x."
Next, we consider the statement "The thousands are double the tens." This means that the thousands digit is twice the value of the tens digit. Since the tens digit is "2x," the thousands digit would be "2(2x)" or "4x."
Now, let's consider the statement "The sum of the digits is 19." This means that the sum of the ones, tens, hundreds, and thousands digits equals 19. Using the variables we defined earlier, we can write an equation:
x + 2x + 2(2x) + 4x = 19
Simplifying the equation gives us:
9x = 19
To solve for x, divide both sides of the equation by 9:
x = 19/9
Since we are looking for a 4-digit number, we need to check whether this value for x satisfies that condition. Since x = 19/9 is not a whole number, it is not a valid digit for our purposes.
Therefore, there is no 4-digit number that satisfies all the given conditions.