the sum of the digits of a two-digit number is 12.the value of the number is equal to 11 times the tens digit. find the number.
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It has.
To find the number, let's break down the problem into steps:
Step 1: Understanding the problem.
We have a two-digit number, and the sum of its digits is 12. Additionally, the value of the number is equal to 11 times the tens digit.
Step 2: Representing the unknowns.
Let's assume the tens digit is represented by 'x' and the units digit by 'y'. Since the number is a two-digit number, the value can be represented as 10x + y.
Step 3: Translating the given information into equations.
Based on the problem description, we have two pieces of information:
1. The sum of the digits is 12: x + y = 12
2. The number is equal to 11 times the tens digit: 10x + y = 11x
Step 4: Solving the equations.
We have two equations:
x + y = 12 (Equation 1)
10x + y = 11x (Equation 2)
Now, we need to solve these equations to find the values of 'x' and 'y' (the tens digit and units digit).
From Equation 1, isolate y:
y = 12 - x
Substituting this into Equation 2:
10x + (12 - x) = 11x
Simplifying and solving for 'x':
10x + 12 - x = 11x
12 = 2x
x = 6
Step 5: Finding the value of the number.
We have found that the tens digit (x) is 6. Now, we can substitute this value of 'x' into Equation 1 to find the units digit (y):
x + y = 12
6 + y = 12
y = 6
So, the units digit (y) is also 6.
Therefore, the number is: 10x + y = 10(6) + 6 = 66.
Hence, the number is 66.