Question

Question:Extended Problem Solving Doctors measure the cholesterol in your blood to see if you are at risk for heart disease. The formula below gives your total cholesterol level in terms of your LDL (or “bad”) cholesterol, your HDL (or “good”) cholesterol, and your triglycerides.

$Total cholesterol=LDL+HDL+\frac{Triglycerides}{5}$

1. When your cholesterol is checked by a doctor, the total cholesterol, HDL cholesterol, and triglycerides are measured directly. The LDL cholesterol is then calculated from these values. Write an equation that you can use to find the LDL level for the patient whose lab results are shown.

1. Solve Find the patient’s LDL level by solving your equation from part (a).
2. Interpret For teenagers, LDL levels below 110 mg/dL are considered acceptable. Levels from 110 mg/dL to 129 mg/dL are borderline, and levels of 130 mg/dL or greater are too high. Classify the LDL level of the given patient as acceptable, borderline, or too high.

Short answer

a. The equation for LDL level of patient is

b. Patient’s LDL level

.

c. Level of LDL of the given patient is at Borderline.

Step-by-step solution

Step-1- Use given formula present in question 

From given information, we came to know that,

$Totalcholesterol=LDL+HDL+\frac{Triglycerides}{5}$

Step-2- Substituting given values

On substituting values, we get

$190=LDL+45+\frac{125}{5}$

Step-3- Conclusion

Therefore, the equation for LDL level of patient is

$190=LDL+45+\frac{125}{5}$

b.Step-1- Use equation that we got in above sub-part 

Step-1- Use equation that we got in above sub-part

Step-2- Substituting given values

On substituting values, we get

$\begin{array}{l}190=LDL+45+\frac{125}{5}\\ 190=LDL+45+25\\ 190=LDL+70\end{array}$

Step-3- Solving for value of LDL

Subtracting on both sides, we get

$\begin{array}{c}190-70=LDL+70-70\\ LDL=190-70\\ LDL=120\end{array}$

Therefore, the patient’s LDL level is .

c.Step-1-Taken from above part

From above part we came to know that patient’s LDL level $=$

$120mg/dL$

Step-2- Checking range of LDL from given information

As the LDL range is in between

$110mg/dLto129mg/dL$

the borderline is given as level of LDL for the patient.

Step-3- Conclusion

The Patient’s LDL level is at borderline.