# Robin earned $4,320 in 9 weeks. How much did he earn working for a full year? (Assume Robin...

## Question:

Robin earned $4,320 in 9 weeks. How much did he earn working for a full year? (Assume Robin worked 50 weeks during the year.)

## 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.

## Answer and Explanation:

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}

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from High School Algebra II: Help and Review

Chapter 1 / Lesson 23