Questions on Word Problems: Linear Equations And Systems Word Problems answered by real tutors!

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Question 153449This question is from textbook Algebra For College Students
: Amber is signing up for cell phone service. She is trying to decide between Plan A, which costs $54.99 a month with a free phone included, and Plan B, which costs $49.99 a month, but would require her to buy a phone for $129. Under either plan, Amber does not expect to go over the included number of monthly minutes. After how many months would Plan B be a better deal? This question is from textbook Algebra For College Students
: Amber is signing up for cell phone service. She is trying to decide between Plan A, which costs $54.99 a month with a free phone included, and Plan B, which costs $49.99 a month, but would require her to buy a phone for $129. Under either plan, Amber does not expect to go over the included number of monthly minutes. After how many months would Plan B be a better deal?
Answer by jojo14344(880) About Me  (Show Source):
You can put this solution on YOUR website!
planA=(54.99/month)+freePHONE
planB=(49.99/month)+129(PHONE)
Let's equate the 2 plans times no. of months "x" for each plan:
planA(x)=PLanB(x)
(54.99/month)(x)=(49.99/month)(x)+129
(54.99/month)(x)-(49.99/month)(x)=129
x((54.99-49.99)/month)=129 ------------> x*((5)/month)=129
x*cross(5)/month(cross(5))=cross(129)25.8/cross(5) , cross multiply:
x=25.8months
Let's try usage of 25months for each plan:
planA:
(54.99/cross(month))(25cross(months))=1374.75
planB:
(49.99/cross(month))(25cross(months))+129=1378.75
IN 25 MONTHS, PLAN A STILL A BETTER CHOICE
Let's try 26 months:
plan A:
(54.99/cross(month))(26cross(months))=1429.74
plan B:
(49.99/cross(month))(26cross(months))+129=1428.74
THERE YOU GO, YOU START SAVINGS IN CHOOSING PLAN B WHEN YOU REACH 26 MONTHS OF USAGE. TRY 36 MONTHS? 48 MONTHS?
Thank you,
Jojo