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The ratio of men to women working for a company is 5 to 6. If there are 168 women working for the...

Question:

The ratio of men to women working for a company is 5 to 6. If there are 168 women working for the company, what is the total number of employees?

Ratios: Identifying Component Values

If a ratio of two measures {eq}x {/eq} and {eq}y {/eq} is given by {eq}x : y {/eq} and we know that the proportion of {eq}x {/eq} corresponds to a specific value {eq}a {/eq}, we can state that {eq}a {/eq} corresponds to a fraction {eq}\dfrac{x}{x + y} {/eq} of the total amount of our quantity. Proportionally, the total amount can be found using cross multiplication.

Answer and Explanation:

Given:

{eq}x : y = 5 : 6 {/eq}

Where:

  • {eq}x {/eq} is the proportion of men
  • {eq}y {/eq} is the proportion of women

We know that a fraction of the total number of employees:

{eq}\dfrac{y}{x + y} = \dfrac{6}{11} {/eq}

Corresponds to 168 women. Let's say that the total number of employees is {eq}n {/eq}. Then we can introduce a proportion: if {eq}\dfrac{6}{11} {/eq} corresponds to 168, then {eq}1 {/eq} corresponds to n:

{eq}\dfrac{168}{\dfrac{6}{11}} = \dfrac{n}{1}\\ n = 168\cdot \dfrac{11}{6} = 308 {/eq}

Thu, the total number of employees in the company is {eq}\boxed{n = 308} {/eq}


Learn more about this topic:

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Ratios and Proportions: Definition and Examples

from Geometry: High School

Chapter 7 / Lesson 1
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