Question

Bayside Insurance offers two health plans. Under plan A, Giselle

would have to pay the first $110 of her medical bills, plus 35% of
the rest. Under plan B, Giselle would pay the first $160, but only
20% of the rest. For what amount of medical bills will plan B save
Giselle money? Assume she has over $160 in bills.

A) Giselle would save with plan B if she had more than $___ in
bills.

Answer 1

Explanation:

Let x represent the amount of medical bills that Giselle has to pay.

Assume she has over $160 in bills,

it means that

x > 160

Under plan A, Giselle would have to pay the first $110 of her medical bills, plus 35% of the rest. Therefore, she will have to pay for

35/100 × (x - 110) = 0.35(x - 110)

Under plan B, Giselle would pay the first $160, but only 20% of the rest. Therefore, she will have to pay for

20/100 × (x - 160) = 0.2(x - 160)

Therefore, the amount of medical bills that plan B will save is

0.35(x - 110) - 0.2(x - 160) = 0.35x - 38.5 - 0.2x + 32

0.15x + 6.5

Substituting x = 160 into 0.15x + 6.5, it becomes

0.15 × 160 + 6.5 = $30.5

Total bills would be 160 + 30.5 = 190.5

Therefore, Giselle would save $30.5 with plan B if she had more than $190.5 in bills.