1. **Problem Statement:** We have a café charging customers based on the number of drinks ordered where $d$ is the number of drinks and $B(d)$ is the total bill. The function $B(d)$ is one-to-one, meaning each number of drinks corresponds to a unique bill amount and vice versa. 2. Since $B(d)$ is one-to-one, it implies that for each $d$, there is a unique $B(d)$ and no two different $d$ values give the same bill. 3. To represent this mathematically, suppose each drink costs a fixed price $p$, then the total bill is given by: $$B(d) = p \times d$$ where $d \geq 0$ and $p > 0$. 4. This function is one-to-one because: - If $B(d_1) = B(d_2)$, then $p \times d_1 = p \times d_2$ - Since $p \neq 0$, dividing both sides by $p$ gives $d_1 = d_2$ 5. Hence, the total bill uniquely determines the number of drinks and vice versa. **Final answer:** The function $B(d) = p \times d$ for some positive price $p$ is one-to-one, representing the total bill based on number of drinks $d$.