## Proportionality Between Variables:

We say that two variables are proportional if their product or ratio is equal to a constant. If the ratio of the variables is equal to a constant, we say that the two variables are directly proportional. If the product of two variables is equal to a constant, we say that the two variables are inversely proportional.

Let Robin's earning be {eq}E {/eq} and the number of weeks worked be represented {eq}x {/eq}. His earning per week can be represented by:

• {eq}\dfrac{E}{x} = k {/eq}

Therefore:

• {eq}E = kx {/eq}

If Robin earned $4,320 in 9 weeks, then: • {eq}4,320 = 9k {/eq} • {eq}\dfrac{4,320}{9} = 480 {/eq} Therefore: • {eq}E = 480x {/eq} For a full year, that is, for {eq}x = 50\; \rm {/eq} weeks, Robin earned: • {eq}E = 480\times 50 {/eq} • {eq}\boxed{\color{blue}{E = \$24,000}} {/eq}