Solving School Ticket Sales Problem with Algebra: A Step-by-Step Guide

Have you ever wondered how to solve real-life problems using algebra? In this article, we will walk through a practical example of solving for the prices of senior citizen and child tickets sold by a school. Let's dive into the problem and see how algebraic methods can provide us with the answers.

Problem Statement

The school sold 3 senior citizen tickets and 9 child tickets for a total of $75 on the first day. On the second day, they sold 8 senior citizen tickets and 5 child tickets for a total of $67. These two equations form a system that we will solve to find the price of each type of ticket.

System of Linear Equations

Let's denote the price of a senior citizen ticket by s and the price of a child ticket by c. The given information can be represented by the following system of linear equations:

3s 9c 75 (Equation 1) 8s 5c 67 (Equation 2)

Solving the System of Equations

First, we will solve one of the equations for one variable in terms of the other. Let's solve Equation 2 for s:

[ 8s 5c 67 ]

[ 8s 67 - 5c ]

[ s frac{67 - 5c}{8} ]

Next, we substitute this expression for s into Equation 1:

[ 3left(frac{67 - 5c}{8}right) 9c 75 ]

[ frac{3(67 - 5c)}{8} 9c 75 ]

[ frac{201 - 15c}{8} 9c 75 ]

[ frac{201 - 15c 72c}{8} 75 ]

[ frac{201 57c}{8} 75 ]

[ 201 57c 600 ]

[ 57c 399 ]

[ c frac{399}{57} 7 ]

Therefore, the price of a child ticket, c, is $7.

Now that we have the value of c, we can substitute it back into one of the original equations to find the value of s. Let's use Equation 2:

[ 8s 5(7) 67 ]

[ 8s 35 67 ]

[ 8s 32 ]

[ s 4 ]

Therefore, the price of a senior citizen ticket, s, is $4.

Let's verify our solution by plugging the values back into both equations:

Equation 1: 3s 9c 75 Equation 2: 8s 5c 67

For Equation 1:

[ 3(4) 9(7) 12 63 75 ]

For Equation 2:

[ 8(4) 5(7) 32 35 67 ]

The solution is correct!

Conclusion

By following the steps outlined above, we successfully determined the prices of the senior citizen and child tickets sold by the school. This problem demonstrates the power of algebra in solving real-world scenarios.

Further Learning

If you are interested in more algebra problems and want to improve your skills, here are some additional resources:

Online math courses that cover algebra Interactive algebra problem solvers and calculators Math forums and communities where you can practice and ask questions

By regularly practicing algebra and solving real-life problems, you can enhance your problem-solving abilities and gain a deeper understanding of mathematical concepts.