need help!! please

Question

A phone company charges a monthly fee of $13$13 plus 1212 cents per text message. Another company charges $20$20 each month plus 88 cents per text message for the same plan.

How many text messages will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone plan from the second company?

Answer 1

the 13 + 12 cents plan is always less expensive and never the same cost as the 20+ 88 cent plan, for any positive numer of text messages

13 + .12t = 20 +.88t

(.88-.12)t = 13-20

.76t = -7

t = -7/.76 = about -9.2105 = about -9 messages

13+.12(-9) = 20+ .88(-9)

13 - 1.08 = 20 -7.92

$11.92 roughly = $12.08, within 16 cents

both plans are an equal cost when a negative 9 text messages are used, if that has any practical meaning

unless you meant 1212 = $12.12 cost per message

then the plans have equal cost when

13 + 12.12t = 20- .88t

(12.12-.88)t = 20-13 = 7

11.24t = 7

t = 7/11.24 = about .623 = about 1 message rounded off to nearest integer

13 +12.12 = 20 +.88

25.12 roughly = 20.88

but the 2nd plan is always cheaper if messages are in integer values