Question

Julianna has a choice of two health care plans. Option A charges $500 for the year and $65 each time she visits the doctor. Option B chargesonly $300 for the year but 595 for each doctor's visit. How many visits will she have to make in a year for Option A to be the better deal?

Answer 1

We need to represent the two options she has:

Option A = 500 + 65 * x

(being "x" the number of times she visits the doctor)

Option B = 300 + 95 * x

this last one is cheaper for the year, but costs more per visit.

We need to find how many visits will make Option A a better deal.

So we start by creating an inequality (we want option A to be a better deal, so to make her spend LESS than option B, and see what number of visits (x) will that correspond to.

So we want: Option A < Option B (option A less than option B)

now we write in math terms:

500 + 65 x < 300 + 95 x

and solve for "x":

subtract 65 x from both sides:

500 < 300 + 95 x - 65 x

500 < 300 + 30 x

subtract 300 from both sides:

500 - 300 < 30 x

200 < 30 x

divide both sides by 30 to isolate "x" (notice that since 30 is a POSITIVE number, the inequality doesn't change direction):

200 / 30 < x

6.666 ... < x

therefore x has to be larger than 6.666...

Therefore, when the number of visits to the doctor reaches "7" she will be already better off with Option A

Answer: Number of visitis must be 7 or more (at least 7)