## Related questions with answers

An average level of HDL, a type of good cholesterol, for a person is usually no more than 60 , and an unhealthy level is lower than 40. A doctor sees 4 patients and tests their HDL levels. The first 3 levels are 45, 52, and 60. What can the fourth patient's HDL level be if the average of all four patients' levels fall in the average, but not unhealthy, range of levels?

Solution

VerifiedLet $x$ be the cholesterol level of the fourth patient. Then, an inequality that models the conditions of the problem is:

$\begin{aligned} 40&\leq\dfrac{45+52+60+x}{4}\leq60\hspace{2cm}\textrm{Simplify} \\ \\ 40&\leq\dfrac{157+x}{4}\leq60\hspace{3.3cm}\textrm{multiply both sides by} 4 \\ \\ 40(4)&\leq157+x\leq60(4)\hspace{3cm}\textrm{Simplify}\\ \\ 160&\leq157+x\leq240\hspace{3.3cm}\textrm{Subtract} 157\\ \\ 160-157&\leq x\leq240-157\hspace{3.3cm}\textrm{Simplify}\\ \\ 3&\leq x\leq83\\ \end{aligned}$

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