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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}

Learn more about this topic:

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Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23
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