Question

Fab Pool Cleaning Service charges $35 per month plus a $50 equipment fee for cleaning the pool. Perfect Pools offers a $40 a month service plus a $35 equipment fee. In how many months will the cleaning costs be the same? What will the cost be?

Answer 1

Hey there!!

Fab pool service costs $35 per month, this is a variable, the number of month could change and $50 for equipment. And perfect pools cost $40( a variable ) and $35 for equipment.

Let's take the number of month as 'm'.

The question asks us to find the number of months at which both of these costs become equal.

As the question states, we will have to equate both the sums or the values.

Total cost = Cost for month + Cost for equipment.

Fab pool :

Cost per month = $35

Cost for equipment = $50

Total cost = 35 × ( the number of months ) + 50

Perfect pools :

Cost for month = $40

Cost for equipment = $35

Total cost = 40 × ( the number of months ) + 35

We have taken the number of months as 'm'.

Now, plugging in the values :

Fab pools : 35m + 50

Perfect pools : 40m + 35

Equating this :

... 35m + 50 = 40m + 35

Subtracting 35m on both sides :

... 50 = 5m + 35

Subtracting 35 on both sides:

... 15 = 5m

Dividing by 5 on both sides :

... m = 3

Hence, the number of months is 3.

Hope it helps!!

Answer 2

In order to solve this problem, we the cost of both to equal each other, so we need to set up two expressions that will equal each other.

Let t = time in months.

The cost of Fab Pool can be represented by the expression 35t + 50

The cost of Perfect Pools can be represented by the expression by 40t + 35.

Now that we have the cost for each, we need to find when they are the same, so we set the expressions equal to each other.

35t + 50 = 40t + 35

Now we solve like a regular equation

50 = 5t + 35

15 = 5t

t = 3

At three months, the cleaning costs will be the same.