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A patient is 72 years old and a heart attack survivor. The patient's doctor tests their heart regularly with an electrocardiogram to ensure their heart has not worsened. The patient's health insurance policy pays as follows:

\begin{tabular}{|l|l|}
\hline Number of Tests & Percent Covered \\
\hline [tex]$1-4$[/tex] & [tex]$65 \%$[/tex] \\
\hline [tex]$5-8$[/tex] & [tex]$70 \%$[/tex] \\
\hline [tex]$9-12$[/tex] & [tex]$75 \%$[/tex] \\
\hline [tex]$13-16$[/tex] & [tex]$80 \%$[/tex] \\
\hline [tex]$\ \textgreater \ 16$[/tex] & [tex]$0 \%$[/tex] \\
\hline
\end{tabular}

If each test costs \[tex]$125 and the patient receives 22 tests, what is the patient's out-of-pocket expense?

A. \$[/tex]362.50

B. \[tex]$262.50

C. \$[/tex]1,450

D. \$1,300

Sagot :

GinnyAnsweridn
To find out the patient's out-of-pocket expense for the 22 electrocardiogram tests, let's follow a step-by-step approach:

1. Calculate the Total Cost:
Each test costs $125, so for 22 tests, the total cost is:
[tex]\[ \text{Total Cost} = 22 \times 125 = 2750 \text{ dollars} \][/tex]

2. Determine the Insurance Coverage:
- For the first 4 tests:
The insurance covers 65% of the cost of these tests.
[tex]\[ \text{Cost per test} = 125 \text{ dollars} \][/tex]
[tex]\[ \text{Total cost for 4 tests} = 4 \times 125 = 500 \text{ dollars} \][/tex]
[tex]\[ \text{Insurance coverage} = 0.65 \times 500 = 325 \text{ dollars} \][/tex]
Hence, the out-of-pocket expense for the first 4 tests is:
[tex]\[ 500 - 325 = 175 \text{ dollars} \][/tex]

- For the next 4 tests (5-8):
The insurance covers 70% of the cost.
[tex]\[ \text{Total cost for 4 tests} = 4 \times 125 = 500 \text{ dollars} \][/tex]
[tex]\[ \text{Insurance coverage} = 0.70 \times 500 = 350 \text{ dollars} \][/tex]
Hence, the out-of-pocket expense for the next 4 tests is:
[tex]\[ 500 - 350 = 150 \text{ dollars} \][/tex]

- For the next 4 tests (9-12):
The insurance covers 75% of the cost.
[tex]\[ \text{Total cost for 4 tests} = 4 \times 125 = 500 \text{ dollars} \][/tex]
[tex]\[ \text{Insurance coverage} = 0.75 \times 500 = 375 \text{ dollars} \][/tex]
Hence, the out-of-pocket expense for these 4 tests is:
[tex]\[ 500 - 375 = 125 \text{ dollars} \][/tex]

- For the next 4 tests (13-16):
The insurance covers 80% of the cost.
[tex]\[ \text{Total cost for 4 tests} = 4 \times 125 = 500 \text{ dollars} \][/tex]
[tex]\[ \text{Insurance coverage} = 0.80 \times 500 = 400 \text{ dollars} \][/tex]
Hence, the out-of-pocket expense for these 4 tests is:
[tex]\[ 500 - 400 = 100 \text{ dollars} \][/tex]

- For the remaining 6 tests (over 16):
These are not covered by insurance.
[tex]\[ \text{Total cost for 6 tests} = 6 \times 125 = 750 \text{ dollars} \][/tex]
Hence, the out-of-pocket expense for these 6 tests is:
[tex]\[ 750 \text{ dollars} \][/tex]

3. Sum the Out-of-Pocket Expenses:
[tex]\[ 175 + 150 + 125 + 100 + 750 = 1300 \text{ dollars} \][/tex]

Thus, the patient's out-of-pocket expense for the 22 tests is:
[tex]\[ \boxed{1300} \][/tex]
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