SOLUTION: hi, i am stuck on this word problem it has taken me all night, if you wouldn't mind helping me, for i can get an idea on what it is. thank you so so much here is the problem. this

Algebra ->  Expressions-with-variables -> SOLUTION: hi, i am stuck on this word problem it has taken me all night, if you wouldn't mind helping me, for i can get an idea on what it is. thank you so so much here is the problem. this       Log On


   

Question 949879: hi, i am stuck on this word problem it has taken me all night, if you wouldn't mind helping me, for i can get an idea on what it is. thank you so so much here is the problem. this is systems using substitution.
your family is trying to decide between two cable companies. satellite systems charges $49 to set the service and $29 per month for basic cable. the other company, communications cable, charges $25 to set up the service and $37 per month for basic table.
a. in how many months will both services cost the same?
b.what will that cost be?
c. which systems should you choose if your family will only need the service for 6 months?




Found 2 solutions by richard1234, MathLover1:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let m be the # of months, C_s be the cost of satellite, and C_c be the cost of communications.
a)
C_s = 49 + 29m
C_c = 25 + 37m

C_s = C_c when 49 + 29m = 25 + 37m, or 24 = 8m --> m = 3.

b) That cost is 49 + 29*3 = $136 (alternatively 25 + 37*3 = $136).

c) You will save money with the satellite systems if you use it for 6 months (plug in m = 6).

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

your family is trying to decide between two cable companies
satellite systems charges $49 to set the service and $29 per month for basic cable
set the linear equation:
let x be the number of the months, and y the cost
y=29x%2B49 ..............satellite systems
the other company, communications cable, charges $25 to set up the service and $37 per month for basic table
y=37x%2B25...........communications cable
a. in how many months will both services cost the same?
29x%2B49=37x%2B25 solve for x
49-25=37x-29x
24=8x
x=3 in 3 months will both services cost the same
b.what will that cost be?
in x=3 months cost will be
y=29x%2B49 ..............satellite systems
y=29%2A3%2B49+
$y=136

y=37x%2B25...........communications cable
y=37%2A3%2B25
y=111%2B25
$y=136

c. which systems should you choose if your family will only need the service for 6 months?
in x=6 months
y=29x%2B49 ..............satellite systems
y=29%2A6%2B49
$y=223

y=37x%2B25...........communications cable
y=37%2A6%2B25
$y=247

if your family will only need the service for 6 months, should choose satellite systems and save $247-223=24