No, ONE isn't 1!

$$\begin{align*} TWO &= 2 \\ SEVEN &= 7 \\ EIGHT &= 8 \\ TEN &= 10 \\ TWENTY &= 20 \\ SEVENTY &= 70 \\ EIGHTY &= 80 \\ ONE &= ? \end{align*}$$

(Source: Brilliant.org (problem page))

The letters are each variables that multiply together to create the end result. The key to starting to solve the problem is to notice in particular that, while $SEVEN$ is equal to seven, $SEVENTY$ is equal to 70. So $TY$ is equal to ten. Then notice dividing the equation $EIGHTY = 80$ by the other equation $EIGHT = 8$ results in $Y = 10$. This means that $T$ is equal to one. Accordingly, because $TEN = 10$, then $EN$ is equal to ten. This means in turn that $TWENTY = TW(10)(10) = 20$. $TW$ is equal to $\frac{1}{5}$. Then $TWO = \frac{1}{5}O = 2$. This means that $O$ is equal to ten. $NE$ has already been figured out, since it's the same as $EN$ due to commutativity. $ONE$ is then equal to 100.