What number when subtracted from 10 is the same number when it is multiplied by 10?

Answer 1

You can write a system of equations to make this easier.

10 - x = y

10 * x = y

We don't know what the "mystery number" is, but we do know that it equals the same thing both ways, so we can write two equations in the same two variables-x is the mystery number, and y is the result both times. In fact, since these equations equal the same thing, we can reduce this to one equation…

10 - x = 10x

…and solve it: 10 = 10x + x

1 = x + (x/10)

1 = (10x/10) + (x/10)

1 = 11x/10

10 = 11x

x = 10/11

So our number is 10/11. You can verify this by trying it in the original question: 10 - 10/11 = 110/11 - 10/11 = 100/11, and 10/1 * 10/11 = 100/11.