The difference between the digits of a two digit number is 1.The number itself is 1 more than 5 times the sum of its digits.If the units digits is greater than the tens digit,find the number.
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To find the number, we can use algebraic equations.
Let's represent the tens digit as "x" and the units digit as "y".
From the given information, we can create two equations:
Equation 1: The difference between the digits of a two-digit number is 1.
This can be represented as: y - x = 1
Equation 2: The number itself is 1 more than 5 times the sum of its digits.
This can be represented as: 10x + y = 1 + 5(x + y)
Now, let's solve these equations step by step.
1. Rearrange Equation 1 to solve for y in terms of x:
y = x + 1
2. Substitute Equation 1 into Equation 2:
10x + (x + 1) = 1 + 5(x + (x + 1))
Simplify the equation:
10x + x + 1 = 1 + 5(2x + 1)
Combine like terms:
11x + 1 = 1 + 10x + 5
Simplify further:
11x + 1 = 10x + 6
3. Subtract 10x from both sides and simplify:
x + 1 = 6
4. Subtract 1 from both sides:
x = 5
Now that we have found the value of x (the tens digit), we can substitute it into Equation 1 to find the value of y (the units digit):
y = x + 1
y = 5 + 1
y = 6
Therefore, the number is 56.
u = t+1
10t+u = 1+5(t+u)
Solving for t and u, we get 34