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

Let $ x $ represent the cost for a member to take the aerobics class, and $ y $ represent the cost for a nonmember.

### Step 1: Write equations based on the given information

1. Three members and three nonmembers together pay $180. This gives the equation:
   \[
   3x + 3y = 180
   \]
   Simplifying:
   \[
   x + y = 60 \quad \text{(Equation 1)}
   \]

2. Five members and three nonmembers together pay $210. This gives the equation:
   \[
   5x + 3y = 210 \quad \text{(Equation 2)}
   \]

### Step 2: Solve the system of equations

From **Equation 1**, solve for $ y $:
\[
y = 60 - x \quad \text{(Substitute this into Equation 2)}
\]

Substitute $ y = 60 - x $ into **Equation 2**:
\[
5x + 3(60 - x) = 210
\]
Expand and simplify:
\[
5x + 180 - 3x = 210
\]
\[
2x + 180 = 210
\]
\[
2x = 30
\]
\[
x = 15
\]

Now, substitute $ x = 15 $ back into **Equation 1**:
\[
15 + y = 60
\]
\[
y = 45
\]

### Step 3: Conclusion

The cost for a member to take the aerobics class is **$15**, and the cost for a nonmember is **$45**.

---

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What if 4 members and 4 nonmembers take the class? How much would they pay?
2. If the price for nonmembers increases by $5, how will the total change for each group?
3. How would the equation change if only 2 members and 3 nonmembers attended?
4. What percentage discount do members receive compared to nonmembers?
5. How much would it cost for a mixed group of 10 members and 5 nonmembers?

**Tip:** When solving a system of equations, substituting one variable into the other is an efficient way to eliminate a variable and simplify the solution.

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

Learn how to solve a system of linear equations to determine the cost for members and nonmembers taking an aerobics class. This problem demonstrates the use of substitution to solve for unknowns based on a real-world scenario involving recreation center fees. Suitable for students in Grades 6-8.

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