1550.29 – Restaurant Bill

Cecile ate a lot at her favorite Chinese restaurant, Be Happy in Your Wok, and then paid her bill. If the bill had been half as much, she would have gotten three times as much change. If the bill had been two dollars more, she would have gotten only half as much change as she actually did get. So how much was her change?

Solution

Let’s say that Cecil paid with a CC-dollar bill. Her food bill was bb, and she got xx in change. So:

C=b+x=b2+3x=b+2+x2\begin{align*}C &= b + x \\&= \dfrac{b}{2} + 3x \\&= b + 2 + \dfrac{x}{2}\end{align*}

Equating b+x=b+2+x2b + x = b + 2 + \dfrac{x}{2}, we get x=2+x2→x=4x = 2 + \dfrac{x}{2} \rightarrow x = 4.

Cecil’s change was $4.

Nothing is said about what kind of a bill (CC) she paid with. Does it matter? Run the numbers for several sized bills – $10, $20, $50, say. What do you conclude?