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>.
