Given:
- $35 is charged per form, but $0 if only the easiest form is filed.
- $2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
- Total amount charged for the full year = $7245
- Total amount donated for the full year = $1242
To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.
Concept:
We can make use of the Unitary Method here. <u>Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.</u>
So,
<u>Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group</u>
Explanation & Calculation:
We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.
So, putting in the values into the expression,
$35 = $7245 ÷ number of $35 forms
Therefore, number of $35 forms = $7245 ÷ $35
Using simple division, number of $35 forms = 207
Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).
If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.
So, putting the values into the expression,
$2 = $1242 ÷ total number of forms
Therefore, total number of forms = $1242 ÷ $2
Using simple division, total number of forms = 621
Conclusion:
Sterre has filed <u>a total of 621 tax returns</u> (both charged and for free).
Of these 621 returns filed, <u>for 207 forms, Sterre charged $35</u>.
The number of returns Sterre filed for free (that is, the easiest forms) is
Total number of forms - Chargeable forms = 621 - 207 = 414
Thus, Sterre filed <u>414 tax returns for free</u>.
filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.