the units of a two-digit number exceeds thrice the tens digit by 1. the sum of the digits is 9. find the number.
follow the method I showed you for your other posts.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the tens digit of the two-digit number is "x", and the units digit is "y."
From the first statement, we can create the equation: "The units of a two-digit number exceeds thrice the tens digit by 1."
This can be written as: y = 3x + 1.
From the second statement, we know that the sum of the digits is 9. Therefore, we can create the equation: x + y = 9.
Now, we have a system of two equations:
1. y = 3x + 1
2. x + y = 9
To find the solution, we can substitute equation 2 into equation 1.
Substituting y in equation 1 with (9 - x) from equation 2, we get:
3x + 1 = 9 - x
Simplifying the equation:
3x + x = 9 - 1
4x = 8
x = 2
Now that we know the value of x, we can substitute it into equation 2 to find y:
2 + y = 9
y = 9 - 2
y = 7
Therefore, the two-digit number is 27.