The Drama Club Is Selling Short-sleeved Shirts For $ 5 \$5 $5 Each And Long-sleeved Shirts For $ 10 \$10 $10 Each. They Hope To Sell All Of The Shirts They Ordered To Earn A Total Of $ 1 , 750 \$1,750 $1 , 750 . After The First Week Of The Fundraiser,

The Drama Club Fundraiser: A Math Problem

The drama club is selling short-sleeved shirts for $\$5$ each and long-sleeved shirts for $\$10$ each. They hope to sell all of the shirts they ordered to earn a total of $\$1,750$. After the first week of the fundraiser, they have sold $x$ short-sleeved shirts and $y$ long-sleeved shirts. The total amount of money they have earned so far is $5x + 10y$.

The Problem

The drama club wants to know how many short-sleeved shirts and long-sleeved shirts they need to sell in order to reach their goal of earning $\$1,750$. They also want to know how many shirts they have sold so far.

The Equation

Let's say the drama club needs to sell $s$ short-sleeved shirts and $l$ long-sleeved shirts to reach their goal. We can set up an equation based on the information given:

$$5s + 10l = 1750$$

We also know that the total number of shirts sold is $s + l$. Since they have sold $x$ short-sleeved shirts and $y$ long-sleeved shirts so far, we can set up another equation:

$$s + l = x + y$$

The Solution

To solve this problem, we can use the method of substitution or elimination. Let's use the elimination method.

First, we can multiply the second equation by $-5$ to get:

$$-5s - 5l = -5x - 5y$$

Now, we can add this equation to the first equation to get:

$$5s + 10l - 5s - 5l = 1750 - 5x - 5y$$

Simplifying the equation, we get:

$$5l = 1750 - 5x - 5y$$

Now, we can divide both sides by $5$ to get:

$$l = \frac{1750 - 5x - 5y}{5}$$

The Answer

The drama club needs to sell $s$ short-sleeved shirts and $l$ long-sleeved shirts to reach their goal. We can substitute the expression for $l$ into the first equation to get:

$$5s + 10\left(\frac{1750 - 5x - 5y}{5}\right) = 1750$$

Simplifying the equation, we get:

$$5s + 3500 - 10x - 10y = 1750$$

Now, we can add $10x + 10y$ to both sides to get:

$$5s + 3500 = 1750 + 10x + 10y$$

Subtracting $3500$ from both sides, we get:

$$5s = 1750 + 10x + 10y - 3500$$

Dividing both sides by $5$, we get:

$$s = \frac{1750 + 10x + 10y - 3500}{5}$$

The Final Answer

The drama club needs to sell $\frac{1750 + 10x + 10y - 3500}{5}$ short-sleeved shirts and $\frac{1750 - 5x - 5y}{5}$ long-sleeved shirts to reach their goal.

The Graph

We can graph the equation $5s + 10l = 1750$ to visualize the solution. The graph is a line with a slope of $-2$ and a y-intercept of $175$.

The Conclusion

The drama club needs to sell a certain number of short-sleeved shirts and long-sleeved shirts to reach their goal of earning $\$1,750$. We can use the method of substitution or elimination to solve this problem. The solution is a linear equation, and we can graph the equation to visualize the solution.

The Future

The drama club can use this information to make informed decisions about their fundraiser. They can adjust their prices or the number of shirts they sell to reach their goal. They can also use this information to plan for future fundraisers.

The Limitations

This problem assumes that the drama club can sell all of the shirts they ordered. In reality, they may not be able to sell all of the shirts, and they may need to adjust their prices or the number of shirts they sell accordingly.

The Real-World Application

This problem has real-world applications in business and economics. Companies often use linear equations to model their sales and revenue. They can use this information to make informed decisions about their pricing and production.

The Mathematical Concepts

This problem involves the following mathematical concepts:

• Linear equations
• Graphing
• Substitution and elimination methods
• Real-world applications of mathematics

The Conclusion

The drama club needs to sell a certain number of short-sleeved shirts and long-sleeved shirts to reach their goal of earning $\$1,750$. We can use the method of substitution or elimination to solve this problem. The solution is a linear equation, and we can graph the equation to visualize the solution. This problem has real-world applications in business and economics, and it involves the following mathematical concepts: linear equations, graphing, substitution and elimination methods, and real-world applications of mathematics.
The Drama Club Fundraiser: A Math Problem Q&A

We've already discussed the drama club's fundraiser and how they can use math to solve the problem. Now, let's answer some frequently asked questions about the problem.

Q: What is the goal of the drama club's fundraiser?

A: The goal of the drama club's fundraiser is to earn $\$1,750$ by selling short-sleeved shirts for $\$5$ each and long-sleeved shirts for $\$10$ each.

Q: How many short-sleeved shirts and long-sleeved shirts does the drama club need to sell to reach their goal?

A: The drama club needs to sell $\frac{1750 + 10x + 10y - 3500}{5}$ short-sleeved shirts and $\frac{1750 - 5x - 5y}{5}$ long-sleeved shirts to reach their goal.

Q: What is the equation that represents the total amount of money the drama club has earned so far?

A: The equation that represents the total amount of money the drama club has earned so far is $5x + 10y$.

Q: How can the drama club use this information to make informed decisions about their fundraiser?

A: The drama club can use this information to adjust their prices or the number of shirts they sell to reach their goal. They can also use this information to plan for future fundraisers.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in business and economics. Companies often use linear equations to model their sales and revenue. They can use this information to make informed decisions about their pricing and production.

Q: What are some limitations of this problem?

A: This problem assumes that the drama club can sell all of the shirts they ordered. In reality, they may not be able to sell all of the shirts, and they may need to adjust their prices or the number of shirts they sell accordingly.

Q: How can the drama club graph the equation $5s + 10l = 1750$ to visualize the solution?

A: The drama club can graph the equation $5s + 10l = 1750$ to visualize the solution. The graph is a line with a slope of $-2$ and a y-intercept of $175$.

Q: What are some mathematical concepts involved in this problem?

A: This problem involves the following mathematical concepts:

• Linear equations
• Graphing
• Substitution and elimination methods
• Real-world applications of mathematics

Q: How can the drama club use this information to plan for future fundraisers?

A: The drama club can use this information to plan for future fundraisers by adjusting their prices or the number of shirts they sell to reach their goal. They can also use this information to make informed decisions about their pricing and production.

Q: What are some potential challenges the drama club may face in their fundraiser?

A: The drama club may face challenges such as not being able to sell all of the shirts they ordered, or not being able to reach their goal. They may need to adjust their prices or the number of shirts they sell accordingly.

Q: How can the drama club overcome these challenges?

A: The drama club can overcome these challenges by being flexible and adjusting their prices or the number of shirts they sell to reach their goal. They can also use this information to make informed decisions about their pricing and production.

Q: What are some potential benefits of the drama club's fundraiser?

A: The drama club's fundraiser can have several benefits, such as raising money for their school, building community spirit, and providing a fun and engaging experience for students.

Q: How can the drama club measure the success of their fundraiser?

A: The drama club can measure the success of their fundraiser by tracking the number of shirts sold, the amount of money raised, and the feedback from students and parents.

Q: What are some potential lessons the drama club can learn from this experience?

A: The drama club can learn several lessons from this experience, such as the importance of planning and preparation, the value of teamwork and collaboration, and the need to be flexible and adaptable in the face of challenges.