the units digit of a 2 digit number is 4 less than the tens digit. the number it names is 3 less than 9 times the sum of the digits what is the number?

let the tens digit be x

then the unit digit is x-4

the number itself is 10x + (x-4)
sum of the digits is x + x-4 = 2x - 4

10x + x-4 = 9(2x-4) -3
11x-4 = 18x - 36 - 3
-7x = -35
x = 5

tens digit is 5, unit digit is 1
the number id 51

Thank you!

To find the number, let's assign variables to the tens and units digits of the number.

Let's say the tens digit is "x" and the units digit is "y".

According to the given information, the units digit is 4 less than the tens digit. This can be represented as:

y = x - 4

The number is also stated to be 3 less than 9 times the sum of its digits. The sum of the digits is x + y. Hence, the number can be expressed as:

10x + y = 9(x + y) - 3

Now, we can substitute the value of y from the first equation into the second equation:

10x + (x - 4) = 9(x + (x - 4)) - 3

Simplifying:

10x + x - 4 = 9(2x - 4) - 3
11x - 4 = 18x - 36 - 3
11x - 4 = 18x - 39
39 - 4 = 18x - 11x
35 = 7x
x = 35/7
x = 5

Now that we have the value of x, we can substitute it back into the first equation to find y:

y = 5 - 4
y = 1

Therefore, the number is 51.