The units digit of a 2 digit number exceeds thrice the tens digit by 1. The sum of the digits is 9. Find the number.

a = first number

b = second number

b = 3 a + 1

a + b = 9

a + 3 a + 1 = 9

4 a + 1 = 9 Subtract 1 to both sides

4 a + 1 - 1 = 9 - 1

4 a = 8 Divide both sides by 4

a = 8 / 4

a = 2

b = 3 a + 1

b = 3 * 2 + 1

b = 6 + 1

b = 7

Your number :

27

27

Ah, solving math problems, huh? Alright, let's engage in some numerical humor!

Well, let's call the tens digit "x" and the units digit "y". According to our problem, we can form the following equations based on the given information:

1. y = 3x + 1 (The units digit exceeds thrice the tens digit by 1)
2. x + y = 9 (The sum of the digits is 9)

Now, let's substitute y in terms of x from the first equation into the second equation:

x + (3x + 1) = 9

Simplifying that:
4x + 1 = 9

Subtracting 1 from both sides:
4x = 8

Dividing both sides by 4:
x = 2

So, the tens digit (x) is 2. Now, let's substitute this back into the first equation to find the units digit (y):

y = 3(2) + 1
y = 7

Putting it all together, the number is 27. Voila!

Let's call the tens digit of the number "x" and the units digit "y".

From the given information:
1. The units digit exceeds thrice the tens digit by 1: y = 3x + 1.
2. The sum of the digits is 9: x + y = 9.

We can solve this system of equations to find the values of x and y.

From equation 2 (x + y = 9), we can rearrange it to get x = 9 - y.

Now substitute this value of x into equation 1 (y = 3x + 1):

y = 3(9 - y) + 1
y = 27 - 3y + 1
4y = 28
y = 7

Now substitute the value of y into equation 2:

x + 7 = 9
x = 9 - 7
x = 2

Therefore, the tens digit is 2 and the units digit is 7. The number is 27.

To find the number, let's assume the tens digit is "x" and the units digit is "y".

From the given information, we can create two equations:

1. The units digit of a 2-digit number exceeds thrice the tens digit by 1:
y = 3x + 1

2. The sum of the digits is 9:
x + y = 9

Now we can solve this system of equations:

We can substitute the value of "y" from the first equation into the second equation:

x + (3x + 1) = 9
4x + 1 = 9
4x = 9 - 1
4x = 8
x = 8/4
x = 2

Now substitute the value of "x" back into the first equation to find "y":

y = 3x + 1
y = 3(2) + 1
y = 6 + 1
y = 7

So the number is 27.