Question

Mona makes and sells handmade board games for $35 each. Each month she donates 3 puzzles to a retirement community. All also makes and sells handmade board games for $29 each. Each month she donates 1 puzzle to a childcare center. Mona and All make the same number of board games each month. The linear functions M(x) = 35(x - 3) and A(x) = 29(x - 1) represent the total amount each girl can earn taking into account the board games that are donated and not sold. Write a linear function that represents the total amount Mona and All can earn.

Answer 1

To calculate the combined earnings of Mona and All, add their individual earnings functions together. This results in T(x) = M(x) + A(x), leading to the linear function T(x) = 64x - 134, which represents their total earnings.

Step-by-step explanation:

The question is asking us to create a linear function that represents the total amount of money Mona and All can earn from making and selling their handmade board games, including the donations they make each month. Given the individual linear functions for Mona and All's earnings, M(x) = 35(x - 3) and A(x) = 29(x - 1), we can combine them to form the total earnings function for both of them together.

To find this combined function, we simply add the two functions together: T(x) = M(x) + A(x). Plugging in the provided functions, we get T(x) = 35(x - 3) + 29(x - 1). Distributing and combining like terms yields T(x) = 35x - 105 + 29x - 29. Simplifying it further, we get T(x) = (35x + 29x) - (105 + 29), which simplifies to T(x) = 64x - 134. This is the linear function that represents the total combined earnings of Mona and All from making and selling their board games, taking into account their donations.