Please !!What should be the right behavior of my subsidiary dental insurance(Premera blue cross)?

I have two dental insurances: Primary is Delta insurance which will cover 80% of total.
Secondary isPrem eraa Blue Cross which will cover 85% of total.
While their allowable amount for each service is different.\
Say I own two services done and the doctor charge 600 of each.Total charges billed by my dentist=1200

For Delta(Primary): the allowed amount is 500 each, next it will pay 500*80%+500*80%= 800. The remaining is 1000-800=200.

For Premera: the allowed amount is 550 for the first service and 450 for the second service.
It will pay 550-400=140?
480-400=80?
Total salaried to my dentist =220 > the remaining amount asked by my first insurance?
Is that the correct way?

If this is correct, what if my secondary insurace's allowable amount is singular 400 each. Then it won't pay my dentist any more. Who will responsible for the remaining 200? Will the dentist bill me?

Please comfort me !!
I think it's ridiculous for Premera, because they use their allowable amount (which could be higher or lower than Delta) as a total. So it wrapping up up overpay the doctor or pay less. It won't settle up exact the remaining amount unless its allowed amount is same as the primary one.
Answers:
Assuming you have no deductible with any plan, for the first service, your primary coverage will pay 80% of $500, or $400, leaving you to pay envelope $100. Your secondary carrier would recompense up to 85% of $550, or $467, minus what your primary paid - so they pay $67. You will enjoy to pay $83 - the difference between the allowable and what was covered.

For the second service, same point - Primary pays $400, leaving a balance for you to settle up of $100. Secondary won't pay anything, because their payable amount is under your primary reward.

Although your goal was probably to not remuneration anything out of pocket, it doesn't work that way in the solid world - you still have to pay. In this defence, your dentist is going to bill you for $183 - which is how much you will owe.
Thank you for your explanation here. I think the reason I choose to hold two insurance is to minimize my out of pocket money. In your calculating methods, the patient has to take-home pay the difference between the maxium allowable amount (which could be the primary allowable amount or the secondary allowable amount, whichever is higher) and what was covered.

Say my dentist charge 800 for my service. If I own only primary insurance which allowable amount is 500 and will cover 80% of it. Then I need to wages the rest 20% of 500 which is 100.

But if I have secondary insurance next to 700 allowable amount for that service(200 higher than the above one). Assuming it also cover 80% of service, then it will reimburse my dentist of 700*80%-400=160. As your calculating methods, the doctor will bill me the rest amount 700-400-160=140, which is even higher then what i requirement to pay if I only own one insurance!


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