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 the digits, if the unit digit is greater than the tens digit, find the number.
I just did one like this for you.
x=8
y=4
the number is 46
To solve this problem, we need to analyze the given information and use algebraic equations to find the solution.
Let's assume the tens digit is represented by 'T' and the ones (or units) digit is represented by 'U'.
From the information given, we know that the difference between the digits is 1. So we can write the equation:
U - T = 1 -------------- Equation 1
We are also given that the number itself is 1 more than 5 times the sum of the digits. The sum of the digits is T + U, so we have:
10T + U = 1 + 5(T + U) --- Substituting the digits into the equation
Simplifying the equation, we get:
10T + U = 1 + 5T + 5U
Rearranging, we have:
10T - 5T - 5U = 1 - U
Combining like terms, we get:
5T - 5U = 1 - U -------------- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously.
Let's substitute the value of U from Equation 1 into Equation 2, to eliminate the variable U:
5T - 5(U + 1) = 1 - U
5T - 5U - 5 = 1 - U
5T - 5U + U = 1 + 5
Simplifying, we get:
5T - 4U = 6 -------------- Equation 3
Now, we can solve the system of equations by solving Equation 1 and Equation 3 simultaneously.
Equation 1: U - T = 1
Equation 3: 5T - 4U = 6
One way to solve this system is by substitution. We solve Equation 1 for U and substitute it into Equation 3:
U = T + 1 --- Equation 1 rearranged
5T - 4(T + 1) = 6 --- Substituting U into Equation 3
Simplifying, we get:
5T - 4T - 4 = 6
T - 4 = 6
T = 6 + 4
T = 10
Now that we have T, we can substitute it back into Equation 1 to find U:
U - 10 = 1
U = 1 + 10
U = 11
Therefore, the number is 10T + U = 10(10) + 11 = 101.