You can break this up into pieces.

The first $1,000 in medical expenses:

Family total = $800 (initial premium) + $200 (20% of expenses) = $1000

Insurance total = $800 (80% of total)

After this the insurance company pays all the expenses and is $200 behind the family total, so an additional $200 must me spent to make the totals equal.

$1,000 + $200 = $1,200

B

j_shreyans wrote:Guys ,

A family pays $800 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total

A. $1,000

B. $1,200

C. $1,400

D. $1,800

E. $2,200

Since the plan pays 80 percent of the first $1,000 in expenses, the family pays 20% of the first $1000 in expenses.
Thus:
The total amount paid by the family = premium + 20% of the first $1000 in expenses = 800 + 200 = 1000.

We can PLUG IN THE ANSWERS, which represent the total amount of medical expenses.
When the correct answer choice is plugged in, the plan will pay the same amount as the family's total ($1000).

D: 1800
Since the plan pays 80% of the first $1000 and 100% of the remainder, the amount paid by the plan = 80% of 1000 + 100% of 800 = 800+800 = 1600.
Too much.
Since the correct answer choice must be SMALLER, eliminate D and E.

B: 1200
Since the plan pays 80% of the first $1000 and 100% of the remainder, the amount paid by the plan = 80% of 1000 + 100% of 200 = 800+200 = 1000.
Success!

The correct answer is B.

A family pays $800 per year for an insurance plan that pays 80 percent of the first
$1,000 in expenses and 100 percent of all medical expenses thereafter. In any given
year, the total amount paid by the family will equal the amount paid by the plan
when the family's medical expenses total.

A. $1,000
B. $1,200
C. $1,400
D. $1,800
E. $2,200

If we let m = total medical expenses incurred by the family and p = total amount paid by family, then p = 800 + 0.2m if m ≤ 1000, or p = 800 + 0.2(1000) = 1000 if m > 1000.

If we let n = total amount paid by the insurance plan, then n = 0.8m if m ≤ 1000, or n = 0.8(1000) + m - 1000 = m - 200 if m > 1000.

We need to determine when n = p. We have two cases: 1) if m ≤ 1000; 2) if m > 1000.

1) If m ≤ 1000, we have:

n = p

0.8m = 800 + 0.2m

0.6m = 800

m = 800/0.6 = 8000/6

We see that m > 1000, which is contradictory to our assumption that m ≤ 1000. So, let's analyze case 2.

2) if m > 1000, we have:

n = p

m - 200 = 1000

m = 1200

We see that m = 1200 is within our assumption that m > 1000. So, if the family's total medical expenses are $1,200, then the family and the insurance company will have paid equal amounts.

Answer: B

Why in ever answer we are assuming that insurance is paying the the family back on the same money?

Family spends 800 > gets nothing back (family money -800)
Family spends 1000 > gets 800 back (family money -1000) - why everyone is saying at this point that insurance will pay 800 again??? They already paid it back....?
Family spends 200 > gets back 200 (family money -1000)

Again even if we say insurance counts 800 as money spend by family:
F spends 800 > nothing back (-800)
F spends 200 > (totals 1000) gets 800 back (f money is -200)
F spends 200 (total jumps to -400) > gets back 200 (-200)

How come insurance is returning money back from the past? Oh you spend 1 dollar today, here is $1000 back based on your total spent?

Like family got 80% discount and paid 200 not 1k, and after that they get $800 for just spening that 200?

How does this world works