2-digit num. has value 1 greater than 8 times sum of digits

[SPL8]

I have the following problem: A two-digit counting number has a value that is 1 greater than 8 times the sum of its digits. If 3 times the tens digit is 11 greater than the units digit, what is the number?

I understand how to do the problem when they give me the sum of the digits, but what do you do when you don't have the sum? My formulas normally would be

T+U=(any number)
10T+U
10U+T

Does anyone know how to do this :!:

 

[Mrspi]

Re: Number Word Problems

I have the following problem: A two-digit counting number has a value that is 1 greater than 8 times the sum of its digits. If 3 times the tens digit is 11 greater than the units digit, what is the number?
I understand how to do the problem when they give me the sum of the digits, but what do you do when you don't have the sum?
My formulas normally would be
T+U=(any number)
10T+U
10U+T
Does anyone know how to do this :!:

If T is the tens digit and U is the units digit, the VALUE of the counting number is 10T + U.

"the value of the number is 1 greater than 8 times the sum of its digits"

10T + U = 8(T + U) + 1

"three times the tens digit is 11 greater than the units digit"

3T = U + 11

Ok...that wasn't so tough! Now the ball is in your court. Solve for T and U.