Question

Verizon charges a $40 sign-up fee and the $60 a month for their new hotspot. T-Mobile

charges $100 sign-up fee and then $45 per month for their new hotspot. After how many
months of service will the two company's fees be the same?

Answer 1

4 months

As we show that ;

40 + (60x * 4) = 280

100 + (45x * 4) = 280

but in simultaneous equations Verizon must be set equal to 240 being 80 x 3

and T mobile must be equal to 45 x 4 = 180

so that 240+ 180 = 420 to find 4

This would be a method on distribution as "60 sign up is 1/3 more than 1st equation.

Explanation:

This is a simultaneous equation but trial and error is below to prove all is true.

step 1 make all equations same

40s + (60x) * 3 = 180x LCM = 80 x 3 = 1 1/3 of 60

100s + (45x) * 4 = 180x LCM = 45 x 4 = 1 of 45 as verizon charges 1/3 more sign up.

100s- 40s + 180x = (180x) = 240 + 180

60s + 180x = 420

s = 60

so our equations must each end with 420

when we get 60s + 180x = 420 then

420 - 180 = 240

240/60 = 4

x = 4 months

Verizon = 1st and T mobile = 2nd

40 + (60x * 5) = 340

100 + 45x * 5 = 325

with $15 out after 5 months so we try 6 months

40 + (60x * 6) = 400

100 + 45x * 6 = 370

and see this is increasing in difference, so try a smaller value of months..

We try 4 months;

40 + (60x * 4) = 280

100 + (45x * 4) = 280

Answer 2

Explanation:

Start Unlimited:

$70 for one line

$60 for two lines

$45 for three lines

$35 for four lines

Play More Unlimited:

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Do More Unlimited:

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Get More Unlimited:

$90 for one line

$80 for two lines

$65 for three lines

$55 for four lines