a) The ratio of total cholesterol to HDL is increased or decreased if the total...

a) Cholesterol level is measured using the ratio of total cholesterol to HDL.
Calculation: At first write the given statement in mathematical terms
cholestrol level $=\frac{totalcholestrol}{HDL}\cdots$ equation (1)
And in case of inverse variation variables are related as
${\displaystyle x\mathrm{\infty }\frac{1}{y}}$
where ${\displaystyle \mathrm{\infty }}$ is the sign of inverse proportion between x and y
And when y is increased x is decreased and vice versa.
In this problem it is asking about the ratio is increased or decreased if the total cholesterol remains the same but the HDL is increased.
From equation (1)
cholestrol level $=\frac{totalcholestrol}{HDL}$
Since HDL is inversely related to cholesterol level so if the HDL is increased and the total cholesterol remains the same the cholesterol level will decreased.
Given:
Cholesterol level is measured using the ratio of total cholesterol to HDL.
The ratio of total cholesterol to HDL should be less than or equal to ${\displaystyle 4.5:1}$
Mile's total cholesterol is 220mh/dL and hid HDL is 50mg/dL.
Calculation:
The ratio of total cholesterol to HDL should be less than or equal to ${\displaystyle 4.5:1}$.
Mike's total cholesterol is 220mg/dL and hid HDL is 50mg/dL.
Cholesterol level is measured using the ratio of total cholesterol to HDL.
At first write the given statement in mathematical terms
cholestrol level $=\frac{totalcholestrol}{HDL}\times$ equation (1)
Substitute the values in above equation
cholestrol level ${\displaystyle =\frac{220}{50}}$
${\displaystyle =\frac{22}{5}}$
${\displaystyle =\frac{4.4}{1}}$
${\displaystyle =4.4:1}$
Since the ratio ${\displaystyle 4.4:1}$ is less than ${\displaystyle 4.5:1}$ and it is recommended that the ratio of total cholesterol to HDL should be less than or equal to ${\displaystyle 4.5:1}$.
So, Mike's cholesterol level is appropriate.