At a recreation and sports facility, 3 members and 3 non members pay total of $180 to take an aerobic class. A group of 5 members and 3  pay $210 to take the same class. How much does it cost members and nonmembers to take an aerobics class

Let the cost for a member to take an aerobics class be denoted by $ x $, and the cost for a non-member be denoted by $ y $.

From the problem, we have two groups and the following information:

- **First group:** 3 members and 3 non-members pay a total of $180. This gives the equation:
  \[
  3x + 3y = 180
  \]

- **Second group:** 5 members and 3 non-members pay a total of $210. This gives the equation:
  \[
  5x + 3y = 210
  \]

### Step 1: Simplify both equations
1. From the first equation, divide both sides by 3:
   \[
   x + y = 60 \quad \text{(Equation 1)}
   \]

2. From the second equation, divide both sides by 3:
   \[
   \frac{5x + 3y = 210}{3} \quad \Rightarrow \quad \frac{5x}{3} + y = 70 \

At a recreation and sports facility, 3 members and 3 non-members pay a total of $180 to take an aerobics class. A group of 5 members and 3 non-members pay $210 to take the same class. How much does it cost members and non-members to take an aerobics class?

Learn how to solve a system of linear equations to find the cost for members and non-members to take an aerobics class. This example uses algebraic methods to solve two equations derived from different pricing scenarios. Suitable for students in Grades 8-10.

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