Four digit decimal between 10 and 20 my tenths digit is twice my tens digit sum of my tenths and my ones digit equals my hundredth digit the sum of all my digits is 11
Let me try to wade through this quagmire of a sentence.
A four digit decimal number lies between 10 and 20.
---> 1x.yz
My tenths digit is twice my tens digit.
---> 1x.2z
The sum of my tenths and my ones digit equals my hundredth digit.
---> 2+x=z **
The sum of all my digits is 11.
1+x+2+z=11
x+z = 8 ***
sub ** into ***
x+2+x = 8
2x=6
x=3 , and then z = 5
the number is 13.25
111238446
Let's break down the information given step-by-step:
1. We need to find a four-digit decimal number between 10 and 20.
- Since we are looking for a four-digit decimal number, the decimal part should be between 0 and 9.
2. The tenths digit is twice the tens digit.
- Let's denote the tens digit as "x". Therefore, the tenths digit would be "2x".
3. The sum of the tenths and ones digit equals the hundredth digit.
- Let's denote the ones digit as "y". Therefore, the tenths digit + ones digit = hundredth digit.
- Mathematically, this can be represented as (2x + y) = (10x + y) - (100z), where z is the hundredth digit.
4. The sum of all the digits is 11.
- Mathematically, this can be represented as (10x + y) + (2x + y) + y + z = 11.
Let's solve the equations:
From the second step:
2x + y = 10x + y - 100z
Simplifying this equation:
y = 8x - 100z
From the fourth step:
(10x + y) + (2x + y) + y + z = 11
Simplifying this equation:
12x + 3y + z = 11
Now we have two equations:
y = 8x - 100z
12x + 3y + z = 11
We can solve these equations simultaneously to find the values of x, y, and z, which will give us the desired four-digit decimal number.
To find the four-digit decimal that meets these conditions, we can break down the given information step by step.
1. The number is between 10 and 20:
Since the number is a four-digit decimal, it cannot be less than 10. Therefore, the number must be greater than or equal to 10.
2. The tenths digit is twice the tens digit:
Let's start by assuming the number is in the form of "a b c d", where a, b, c, and d represent the thousands, hundreds, tens, and ones digits respectively.
From the given information, we know that b (the tenths digit) is twice the value of c (the tens digit). So, we can represent this as:
b = 2c
3. The sum of the tenths and ones digit equals the hundredth digit:
According to the given information, b + d = c. We can substitute b with 2c from the previous equation:
2c + d = c
4. The sum of all digits is 11:
From the number in the form "a b c d", we know:
a + b + c + d = 11
Now, let's solve these equations simultaneously to find the values of the digits.
Substituting 2c from equation (2) into equation (3), we have:
2c + d = c
d = -c
Now we can substitute the value of d into the equation (4):
a + b + c + d = 11
a + b + c + (-c) = 11
a + b = 11
From equation (1), we know that:
b = 2c
We can substitute this into the equation (3):
2c + d = c
2c + (-c) = c
c = 0
Using this information, we can substitute c = 0 into the other equations:
b = 2(0) = 0
d = -(0) = 0
a + 0 = 11
a = 11
Therefore, the four-digit decimal that satisfies the given conditions is 1100.