How do I translate the sentence
Four times as many cars were bought as planes.
into an equation?
My teacher told me that this was $c = 4p$, $c$ representing cars and $p$ representing planes. I thought it was $p = 4c$, but according to her I am incorrect. Can someone explain which one is right and why?
$p$ doesn't represent "planes." It represents the number of planes bought. For example, if 5 planes are bought, then $p=5$.
$c$ doesn't represent "cars." It represents the number of cars bought. For example, if 12 cars are bought, then $c=12$.
According to the word description given, "four times as many cars were bought as planes." This could be more clearly expressed as "the number of cars boaught is four times the number of planes bought."
Examples of this might be $p=7$ and $c=28$.
It should then be clear that the correct mathematical relationship between the variables is $c=4p$ and your teacher is correct.