Let's solve the problem step-by-step.

Problem Summary

• A baseball team raised $2,400 from selling balloons and banners.
• The amount earned from balloons and banners was equal.
• Each balloon sold for $3, and each banner sold for $4.
• We need to find how many of each were sold.

Solution

1. Define Variables:

   • Let $x$ be the number of balloons sold.
   • Let $y$ be the number of banners sold.

2. Set Up Equations:

   • Since the total revenue from both items is $2,400: $3x + 4y = 2400$
   • The revenue from balloons is equal to the revenue from banners: $3x = 4y$

3. Solve the Equations:

   • From the second equation, solve for $x$ in terms of $y$: $x = \frac{4y}{3}$
   • Substitute $x = \frac{4y}{3}$ into the first equation: $3\left(\frac{4y}{3}\right) + 4y = 2400$ Simplify: $4y + 4y = 2400$ $8y = 2400$ $y = 300$
   • Substitute $y = 300$ back into the equation $x = \frac{4y}{3}$: $x = \frac{4 \cdot 300}{3} = 400$

Conclusion

The baseball team sold:

• 400 balloons
• 300 banners

Would you like further details on any part of this solution?

Related Questions:

1. What if the price of banners changed to $5? How would that affect the solution?
2. How can we check if the solution is correct?
3. What is the total revenue generated by each item individually?
4. How would the solution change if the revenue from balloons was twice that of banners?
5. What if they raised $3,000 instead of $2,400?

Tip:

When solving systems of equations, substituting one variable in terms of another often simplifies the process.