Hi,
I have had to work on several of these types of problems with no success. Could someone help me make the process easier? I have spent many hours with inconsistent results.
A company offers their employees two medical insurance plans; Plan A has a $130 deductible with a 25% interest on the rest of the bills. Plan B has a $180 deductible with 20% interest on the rest of the bills. An employee would save with Plan B if they had more than ?$ in Bills?
To determine the amount of medical bills at which an employee would save with Plan B, we need to compare the costs between Plan A and Plan B. Here's a step-by-step guide on how to calculate the threshold:
1. Calculate the cost of Plan A:
- Add the deductible ($130) to the percentage of the remaining bills (75% since the interest is 25%).
- For example, if the total bills are "x," the cost with Plan A would be: $130 + 0.75x.
2. Calculate the cost of Plan B:
- Add the deductible ($180) to the percentage of the remaining bills (80% since the interest is 20%).
- The cost with Plan B would be: $180 + 0.8x.
3. Set up an inequality to compare the costs of Plan A and Plan B:
- The employee would save with Plan B if the cost with Plan B is less than the cost with Plan A.
- Formulate the inequality as follows: $180 + 0.8x < $130 + 0.75x.
4. Solve the inequality to find the threshold amount of medical bills:
- Start by simplifying the equation: 0.8x - 0.75x < $130 - $180.
- Combine like terms: 0.05x < -$50.
- Isolate x by dividing both sides by 0.05: x < -$50 ÷ 0.05.
- The answer is x < -$1000.
Therefore, an employee would save with Plan B if they had more than $1000 in medical bills.