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

Mathematics

1 answer:

LiRa [457]4 years ago

4 0

Answer:

Step-by-step 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.

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Ghella [55]

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3 years ago

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mote1985 [20]

recalling that d = rt, distance = rate * time.

we know Hector is going at 12 mph, and he has already covered 18 miles, how long has he been biking already?

$\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 12&1\\ 18&x \end{array}\implies \cfrac{12}{18}=\cfrac{1}{x}\implies 12x=18\implies x=\cfrac{18}{12}\implies x=\cfrac{3}{2}$

so Hector has been biking for those 18 miles for 3/2 of an hour, namely and hour and a half already.

then Wanda kicks in, rolling like a lightning at 16mph.

let's say the "meet" at the same distance "d" at "t" hours after Wanda entered, so that means that Wanda has been traveling for "t" hours, but Hector has been traveling for "t + (3/2)" because he had been biking before Wanda.

the distance both have travelled is the same "d" miles, reason why they "meet", same distance.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hector&d&12&t+\frac{3}{2}\\[1em] Wanda&d&16&t \end{array}\qquad \implies \begin{cases} \boxed{d}=(12)\left( t+\frac{3}{2} \right)\\[1em] d=(16)(t) \end{cases}$

$\bf \stackrel{\textit{substituting \underline{d} in the 2nd equation}}{\boxed{(12)\left( t+\frac{3}{2} \right)}=16t}\implies 12t+18=16t \\\\\\ 18=4t\implies \cfrac{18}{4}=t\implies \cfrac{9}{2}=t\implies \stackrel{\textit{four and a half hours}}{4\frac{1}{2}=t}$