SYSTEM OF EQUATIONS IN THE REAL WORLD
A system of equation is a collection of two or more equations that involve the same set of unknown. These equations can be used to determine the most suitable method for a targeted outcome or to explain an outcome (Birkhoff and Clane 1). They can be solved using substitution, elimination, or graphing method (James 1880). We will discuss an example of a real-world problem with multiple variables that could be solved using an equation system via the substitution method.
Problem:
As a student, I need a loan of $36,550 from two banks to pay for my tuition. Standard knowledge states that each bank has different interests, which help to determine which one to pick. Since my mother is a member of the Carolina Foothills Federal Credit Union, I have been considered for the loan that I applied. What attracted me to this union is the fact that the interest rate is 7.5%, and also that my mother is a member, meaning it would not be hard for them to trust me. Discover bank is my other option, which has an interest rate of 8%. I chose this bank because they offer 1% cash rewards to students who do well in their studies. The bank allows me an early repayment assistance program that helps me hold off on repayments during the first semester of my loan. Considering my financial situation, I am willing to pay total interest of $2,821.25, which will ensure that I am not put into a lot of pressure. The systems of equation will help me calculate the principal amount that I should take from both banks, depending on the interest rates that both offer.
Solution
Identify and name what we are looking for then translate them into two equations;
Let the principal amount for bank one be X;
Let the principal amount for bank two be Y;
x + y = 36550
0.075x + 0.08y = 2821.25
Solve for one variable using one of the equations then substitute its value into the other equation;
X + y -y = 36,550 -y, X = 36,550 – y
0.075 (36550 – y) + 0.08y = 2821.25, 2741.25 – 0.075y + 0.08y = 2821.25,
– 0.075y + 0.08y = 2821.25 – 2741.25, 0.005y/0.005 = 80/0.005,
Y = 16,000
Substitute this value of y into one equation to find the value of X;
X + 16,000 = 36,550,
X = 36,550 – 16,000,
X = 20,550
Carolina Foothills Federal Credit Union principal amount should be $20,550
Discover bank principal amount should be $16,000
Works Cited
Birkhoff, G., And Clane, S. A Survey of Modern Algebra, 3rdd. Macmillan, New York, 1965.
James, J.’ Some functional equations.’ Advances in Algebra, 315 (8), pp.1880-1899. 2006.