Question

Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she donates $ 2 $2dollar sign, 2 to clean water projects per tax return she files. Sterre charged $ 7 , 2 4 5 $7,245dollar sign, 7, comma, 245 and made a donation of $ 1 , 2 4 2 $1,242dollar sign, 1, comma, 242 this year for the tax returns she filed.

Answer 1

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. 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.

So,

Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group

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 a total of 621 tax returns (both charged and for free).

Of these 621 returns filed, for 207 forms, Sterre charged $35.

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 414 tax returns for free.