Often times experienced mathematicians tend to get comfortable with certain problem-solving strategies. For example, in a problem one might use a system of equations to solve a problem rather than employing a simpler more easy way to solve it. Though using system of equations are great, knowing how to solve problems using different approaches is important, not just for oneself, but for their students. Take for example the following problem: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there? Solution 1: (Using Algebra System of Equations) 4p+2c=78 (pigs have 4 feet and chickens have 2 feet with 78 feet in total) p+c=27 (27 heads mean that the number of chicken and pigs total 27) Then by algebra p=27-c. Therefore by substitution, 4(27-c)+2c=78. 108-2c=78. 2c=30. c=15. Since, c=15, p+c=p+15=27. p=12. Therefore, the farmer has 15 chickens and 12 pigs... read more