Linear Systems have many applications in financial topics. In many of the Problems of the Week the applications center around finding how much particular items cost give two or more total costs. The example below is a nice application. In Choosing Charity, students are asked to set up a system of linear equations to examine how much a particular company would contribute to a disaster relief fund based on how much their employees contribute.

Highlighted Problem: Choosing Charity

In the wake of the recent tsunami, a company decided to donate to a disaster relief fund. The company started by pledging a certain amount of money. To encourage their 60 employees to make individual contributions, the company pledged to also donate an additional fixed amount for each employee who made a personal donation to the fund.


The company treasurer determined that if one-third of the employees chose to make a donation, the company’s part of the total donation would be $7000. If 50% of the employees donated, the company’s part of the total donation would be $7750.


  1. Find an equation that expresses the company’s part of the total donation in terms of the number of employees who donate.
  2. If every employee chose to donate, what would the company’s part of the total donation be?
  3. If the company’s part was $8875, what percent of the employees chose to make personal donations?
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