Word problems involving systems of equations are practical. They allow you to figure out individual prices when only totals are known, or determine optimal mixtures of different ingredients in chemistry or cooking.
The key to solving word problems is replacing the unknown values with 'x' and 'y', and creating two distinct equations based on the conditions given.
Be careful not to mix up the variables! If x is the price of an adult ticket and y is the child ticket, make sure you don't accidentally multiply the adult count by y. Always label what x and y represent.
Read the problem, define x and y, and complete the equations.
[Problem] Admission to a park is 4000 yen for 2 adults and 3 children, and 3500 yen for 1 adult and 4 children.
Choose the correct equation for the sentence!
In ancient times before algebra, people solved these types of problems using logic and trial-and-error, a method called the 'rule of false position'. Algebra gives us a direct and foolproof way to find the answer!