the different between the digit of a two digit number is 1, the number it self is 1 more than 5 times the sum of its digits, if the unit digit is greater than the tens digit, find the number.
87
To find the number that satisfies the given conditions, let's break down the problem step by step:
Step 1: Understand the given conditions.
The first condition states that the difference between the digits of the two-digit number is 1. Let's represent the tens digit as 'x' and the units digit as 'x+1'.
The second condition states that the number itself is 1 more than 5 times the sum of its digits. Mathematically, it can be written as:
10x + (x+1) = 5(x + (x+1)) + 1
Step 2: Simplify the equation.
Simplifying the equation, we get:
10x + x + 1 = 5(2x + 1) + 1
11x + 1 = 10x + 6
Step 3: Solve the equation.
Subtracting 10x from both sides, we get:
11x - 10x + 1 = 6
x + 1 = 6
Step 4: Find the value of x.
Subtracting 1 from both sides, we get:
x = 5
Step 5: Check the condition given in the problem.
The condition states that the unit digit should be greater than the tens digit. Substituting the value of x, we have:
x+1 = 5+1 = 6 > x = 5
Step 6: Find the number.
The number we are looking for is formed by the tens digit (x = 5) and the units digit (x+1 = 6). So, the number is 56.
Therefore, the number that satisfies the given conditions is 56.