# What is meant by the phrase constant of proportion?

Oct 21, 2015

When two variables are in proportion, it means that if one gets bigger so does the other, and if one gets smaller so does the other.

For example, if an apple costs 2$, then the more apples you'll buy, the more money you'll spend. Also, if a cinema ticket costs 10$, then the more tickets you'll buy, the more money you'll spend.

But in the first case, the money you pay will be twice the number of apples you've bought, while in the second case the money you spend will be ten times the number of tickets.

So, as long as the behaviour is the same (the more items, the more money spent), you can see that the price of tickets grows much faster than the one of the apples. This is the constant of proportion.

If we call the money spent $s$, the number of tickets $t$, and the number of apples $a$, then in both cases we have

$s = k \cdot t$ and $s = k \cdot a$, but the value of $k$ changes: namely,

$s = 10 t$ and $s = 2 a$. So, ten and two are the constants of proportion.