**Real World Applications of Systems of Equations**

In Many situations that we encounter in our daily lives tend themselves to be solved using a system of equations. Many of these problems are solvable without a system of equations, but it will take more time and effort. Using a system of equations helps you put all your constraints in two or three equations and by solving the system you automatically find the value of what you are looking for. Lets look at an example that many of us encounter.

**The admission fee at a movie theater is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the theater and $5050 is collected. How many children and how many adults attended?** **Step 1:** Decide on your variables.

C=children, A=adults**Step2:** Set up a system of equation that represents the price and the number of people

Price equation: 1.5C + 4A = 5050

#of People: C+A=2200**Step 3:** Solve the system using any method of your choice. (Here I will use substitution)

1. Solve C+A=2200 for C. C=2200-A

2. Substitute C=2200-A into the price equation

1.5(2200-A) + 4A = 5050

3300 - 1.5A + 4A = 5050

2.5A=1750

** A= 700 (700 Adults came to the theater that day)**

3. Plug A=700 back in any of the original two equations

C + 700 = 2200

**C= 1500 (1500 Children came to the theater that day)**

**For You to Try!**

Mary bought a bag of mixed candy. The bag contains two kinds of her favorite candy, Twix and Kit-Kat. Mary knows that each twix weights .75lb and each Kit-Kat weights .50lb each. The total weight of the bag is 21lbs. The bag contains 32 pieces of candy all together. Whithout emptying the bag how many Twix and How many Kit-Kats are in the bag? (Answer: 20 Twix, 12 Kit-Kats)