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Chapter 1: Problem 37

Michelle had a medical bill of $$\$ 850$$. After she paid the deductible of $$\$ 500$$, her insurance company paid \(80 \%\) of the remainder. How much more of the bill did Michelle have to pay? A. 70 B. 100 C. 170 D. 280

Short Answer

Expert verified
A. 70

Step by step solution

01

Find the remainder after the deductible

First, we need to find the amount Michelle still needs to pay after her deductible. To do this, we'll subtract the deductible from her total medical bill: Remainder = Total bill - Deductible
02

Calculate 80% of the remainder

Next, we need to find how much the insurance will cover by calculating 80% of the remainder. To do this, we'll multiply the remainder by 80%: Insurance coverage = Remainder * 80%
03

Calculate the amount Michelle still has to pay

Now, we need to calculate how much more Michelle has to pay. To do this, we'll subtract the insurance coverage from the remainder: Amount Michelle has to pay = Remainder - Insurance coverage
04

Complete the calculations and choose the correct answer

Now, we have all the information necessary to solve the problem: Total bill: $850 Deductible: $500 Remainder: \(850 - \)500 = $350 Insurance coverage: \(350 * 80% = \)350 * 0.8 = $280 Amount Michelle has to pay: \(350 - \)280 = $70 So, the correct answer is: A. 70

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Deductible Calculation
A deductible is an amount you pay for health care services before your health insurance begins to pay. In Michelle's case, her medical bill was $850, and her deductible was $500. This means she needed to pay the first $500 of her medical bill out of her own pocket. Only after this deductible has been paid does her insurance company step in to cover a portion of the remaining costs.

Subtracting the deductible from the total bill lets us figure out how much is left for the insurance to consider.
  • Original medical bill: $850
  • Deductible: $500
  • Remainder after deductible: $850 - $500 = $350
So, the remainder that the insurance company looks at after Michelle paid her deductible is $350.
Mastering Percentage Calculation
Percentage calculations are key to figuring out how much the insurance company will cover from the remainder of the bill. In this problem, we're told that Michelle's insurance covers 80% of the costs that remain after the deductible.

To calculate 80% of the remainder, follow these steps:
  • Convert the percentage to a decimal for easy multiplication: 80% becomes 0.8.
  • Multiply the decimal by the remainder: $350 * 0.8.
  • This yields the amount the insurance will pay: $280.
Therefore, 80% of $350, the amount left after the deductible, equals $280, which is the portion that the insurance company contributes.
Breaking Down Insurance Payment
Insurance payment refers to the part of the bill the insurance covers after a deductible and percentage calculation. For Michelle, it is essential to know how much of the bill she still needs to pay, even after insurance.

After the insurance covers its share, we subtract that amount from the remainder of the bill:
  • Total remainder after deductible: $350
  • Insurance payment: $280
  • Amount for Michelle to pay: $350 - $280 = $70
Thus, Michelle has to cover $70 of her medical bill out of her own pocket after the insurance company has paid its 80% portion. This understanding helps in budgeting for medical expenses as it clarifies both the coverage and the out-of-pocket costs.

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