Problem solving stategy algebra problem 4?

Question

The cube of a whole number is 100 more than the square of the same number. What is the number? How did you get the answer?

Answer 1

x^3 = 100 + x^2
x^3 - x^2 = 100
x^2(x - 1) = 100

You have to find a number where the square of the number times one less than the number is 100. There aren't too many combinations of numbers that have a product of 100. For example, 100 = 50(2) or 25(4) or 10(10). The only one of the group with a perfect square number is 25(4).

If x = 5, it works.

Answer 2

change the problem to variables, x^3 = x^2 + 100

solve for x, answer is 5.. 5 cubed is 125, 5 squared it 25

25 + 100 = 125

Answer 3

The answer is five and i got it from random guessing. 5 times five is 25 but 5^3 is 125