You have budgeted $1300 to have your pool cleaned this summer while you complete the rest of the yard. Dream Pools charges a onetime fee of $550 for supplies and maintenance and then $40 for each service call. Write an inequality that illustrates the problem and solve to find the possible number of times you can have Dream Pools clean your pool within your budget. Show your work and explain your thinking. Make sure to express your answer as an inequality.
To find the possible number of times you can have your pool cleaned within your budget, we need to use an inequality. Let's assume the number of times you have the pool cleaned is represented by the variable 'x'.
The one-time fee for supplies and maintenance is $550, and each service call costs $40. So, the total cost for x number of service calls would be:
Cost of supplies and maintenance: $550
Cost of service calls: $40 * x
Therefore, the total cost of x number of service calls can be represented as:
Total cost = Cost of supplies and maintenance + Cost of service calls
Total cost = $550 + ($40 * x)
Since you have budgeted $1300 for the pool cleaning, the inequality can be written as:
$550 + ($40 * x) ≤ $1300
Now, let's solve this inequality to find the possible number of times you can have Dream Pools clean your pool within your budget:
$550 + ($40 * x) ≤ $1300
Subtract $550 from both sides:
$40 * x ≤ $1300 - $550
$40 * x ≤ $750
Divide both sides by $40:
x ≤ $750 / $40
x ≤ 18.75
Since you can't have a fraction of a service call, you can conclude that the possible number of times you can have Dream Pools clean your pool within your budget is 18 or less.
Therefore, the inequality that illustrates the problem is: x ≤ 18.