Daniel works at an electronics store, and he claims that the popularity of a toaster (measured in number of sales) is inversely proportional to its cost. If 12 customers buy a toaster that costs $\$500$, according to Daniel's theory, how many customers would buy a toaster that costs $\$750$?
I know that inverse proportionality means that the product of the two quantities is constant, so I can write an equation that relates the number of customers and the cost of the toaster. Let $n$ be the number of customers and $c$ be the cost of the toaster. Then, according to Daniel's theory, $n \cdot c = k$ for some constant $k$. I can use the given data to find the value of $k$. If 12 customers buy a toaster that costs $\$500$, then $12 \cdot 500 = k$, so $k = 6000$. Now, I can plug in the new cost of $\$750$ and solve for $n$. I have $n \cdot 750 = 6000$, so dividing both sides by $750$, I get $n = \frac{6000}{750} = 8$. Therefore, according to Daniel's theory, 8 customers would buy a toaster that costs $\$750$. 