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31 March, 20:49

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.

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  1. 31 March, 22:19
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    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.
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