You are choosing between two different cell phone plans. the first plan charges a rate of 24 cents per minute. the second plan charges a monthly fee of $34.95 plus 12 cents per minute.
let
t
be the number of minutes you talk and
c
1
and
c
2
be the costs (in dollars) of the first and second plans. give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans (round your answer to one decimal place)

291.25 talk minutes would produce the same cost for both plans.

Step-by-step explanation:

Both plans can be modeled by a first order equation in the following format:

In which is the initial cost, f is the fee that is paid for each minute, and t is the number of minutes.

Cost of the first plan:

The problem states that the first plan charges a rate of 24 cents per minute, which means that .There is no initial cost, so .

The equation for this plan is:

Cost of the second plan:

The problem states that the second plan charges a monthly fee of $34.95 plus 12 cents per minute. So and

The equation for this plan is:

Find the number of talk minutes that would produce the same cost for both plan:

This is the instant t in which:

291.25 talk minutes would produce the same cost for both plans.

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.