### Instruction: What digit is represented by $\Delta$ if $144 / \Delta = 1\Delta$, with 1 the tens digit and $\Delta$ the ones digit of the quotient?### Response: To solve this problem, I need to find a single digit that satisfies the equation $144 / \Delta = 1\Delta$.
One way to do this is to try different values for $\Delta$ and see if they work.
For example, if $\Delta = 1$, then $144 / \Delta = 144$, which does not have the form $1\Delta$.
If $\Delta = 2$, then $144 / \Delta = 72$, which also does not have the form $1\Delta$.
If $\Delta = 3$, then $144 / \Delta = 48$, which also does not have the form $1\Delta$.
If $\Delta = 4$, then $144 / \Delta = 36$, which also does not have the form $1\Delta$.
If $\Delta = 5$, then $144 / \Delta = 28.8$, which is not even an integer.
If $\Delta = 6$, then $144 / \Delta = 24$, which also does not have the form $1\Delta$.
If $\Delta = 7$, then $144 / \Delta = 20.5714\ldots$, which is not an integer.
If $\Delta = 8$, then $144 / \Delta = 18$, which has the form $1\Delta$.
Therefore, $\Delta = 8$ is the only digit that satisfies the equation.