SOLUTION: Determine when the cost of the two services will be the same amount, and what the price will be. The Strauss family is deciding between two lawn-care services. Green Lawn charg

Algebra ->  Expressions-with-variables -> SOLUTION: Determine when the cost of the two services will be the same amount, and what the price will be. The Strauss family is deciding between two lawn-care services. Green Lawn charg      Log On


   

Question 1171637: Determine when the cost of the two services will be the same amount, and what the price will be.

The Strauss family is deciding between two lawn-care services. Green Lawn charges a $51 startup fee plus $27 per month. Yard Guard charges a $26 startup fee plus $32 per month.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
green lawn equation is a = 51 + 27x
yard guard equation is b = 26 + 32x

they will be equal when a = b.
this happens when 51 + 27x = 26 + 32x.
subtract 26 from both sides of that equation and subtract 27x from both sides of that equation to get:
51 - 26 = 32x - 27x
combine like terms to get:
25 = 5x
solve for x to get:
x = 25/5 = 5
confirm by replacing x with 5 in both equations to get:
51 + 27*5 = 26 + 32*5
this becomes:
186 = 186, confirming the value of x is good.
your solution is that the cost will be the same in 5 months.
after that point, the lawn service that charges 51 + 27 per month will be cheaper.
this can be seen on the following graph.
y = 51 + 27x is in red.