I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?

18.

Step-by-step explanation:

If the tens digit is x^3 the unit digit is x^3 + 7

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).

11x^3 < 93

x^3 < 8 5/11

x <  2.04

As x must be an integer it is either 1 or 2.

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.

The answer is 1  and (1+7)  = 18.

18.  

Step-by-step explanation:  

If the tens digit is x^3 the unit digit is x^3 + 7  

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).  

11x^3 < 93  

x^3 < 8 5/11  

x <  2.04  

As x must be an integer it is either 1 or 2.  

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.  

The answer is 1  and (1+7)  = 18.

step-by-step explanation: