Question

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?

Answer 1

18.

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.

Answer 2

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.