In A Two Digit Number, The Sum Of The Digits Is 14. Twice The Tens Digit Exceeds The Units Digit By One.Find the Numbers.
unit digit --- x
tens digit --- y
x+y = 14
y = 14-x
2y - x = 1
2(14-x) - x = 1
28 - 2x - x = 1
27 = 3x
x = 9
then y = 14-9 = 5
the number is 59
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To find the two-digit numbers that meet the given criteria, we can set up algebraic equations based on the problem description:
Let's assume the tens digit is represented by the variable "x," and the units digit is represented by the variable "y."
According to the problem's first condition, the sum of the digits is 14. Hence, we have the equation: x + y = 14.
According to the second condition, twice the tens digit exceeds the units digit by one. This gives us the equation: 2x = y + 1.
Now, we need to solve these simultaneous equations to find the values of x and y.
We can solve the first equation for x by rewriting it as: x = 14 - y.
Substituting this into the second equation, we get: 2(14 - y) = y + 1.
Simplifying this equation, we have: 28 - 2y = y + 1.
Combining like terms, we get: 3y = 27.
Solving for y gives us: y = 9.
Substituting this back into the first equation, we find: x + 9 = 14, which means x = 5.
Therefore, the two-digit number is 59, as the tens digit is 5 and the units digit is 9.
So, the required number is 59.