Percents: Overview

At a certain company, one-third of the workers do not have a retirement plan. 40% of the workers who do have a retirement plan are in sales, and 20% of the workers who do not have a retirement plan are not in sales. If 120 of the company's workers are in sales, how many of the workers are not?

Complete the No Plan row and use the Sales column to form an equation for $$x$$. Once you know $$x$$, use the Total row to find the answer.

	Sales	No Sales	Total
Plan	$$0.8x$$		$$2x$$
No Plan	$$0.8x$$	$$0.2x$$	$$x$$
Total	120	?	$$3x$$

The Sales column tells you that > $$0.8x + 0.8x = 120$$ > $$1.6x = 120$$ > $$\displaystyle x = \frac{120}{1.6} = \frac{1{,}200}{16} = \frac{300}{4} = 75$$ So the Total/Total is $$3x = 3(75) = 225$$. That makes Total/No Sales equal to $$225 - 120 = 105$$.

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Correct. [[snippet]] Set the **"Plan/No Plan" - "Sales/No Sales"** table so: . . . one-third of the workers do not have a retirement plan. Put $$x$$ in the No Plan/Total box, and $$3x$$ in the Total/Total box. Note that this means that the Plan/Total is the remaining $$2x$$. 40% of the workers who do have a retirement plan are in sales Since the Total/Plan is already filled with $$2x$$, put $$0.4(2x) = 0.8x$$ in the Plan/Sales box. . . . 20% of the workers who do not have a retirement plan are not in sales. Put $$0.2x$$ in the No Plan/No Sales box. If 120 of the company's workers are in sales . . . Put 120 in the Sales/Total box. . . . how many of the workers are not? Place the ? in the No Sales/Total box.

	Sales	No Sales	Total
Plan	$$0.4(2x) = 0.8x$$		$$2x$$
No Plan		$$0.2x$$	$$x$$
Total	120	?	$$3x$$

80

95

105

120

210

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