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.