Question 1171637
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.
<img src = "http://theo.x10hosting.com/2020/121101.jpg" >