Monica's School Band Held A Car Wash To Raise Money For A Trip To A Parade In New York City. After Washing 125 Cars, They Made $ 775 \$775 $775 From A Combination Of $ 5.00 \$5.00 $5.00 Quick Washes And $ 8.00 \$8.00 $8.00 Premium Washes.Let X X X

Monica's School Band Car Wash Fundraiser: A Math Problem

Monica's school band is known for their enthusiasm and dedication to their craft. Recently, they organized a car wash event to raise funds for a trip to a parade in New York City. The event was a huge success, with the band members washing 125 cars and collecting a total of $\$775$. But how did they manage to make such a significant amount of money? In this article, we will delve into the math behind the car wash fundraiser and explore the combination of quick washes and premium washes that contributed to their success.

Let's assume that the band members sold a combination of quick washes and premium washes. The quick washes were priced at $\$5.00$ each, while the premium washes were priced at $\$8.00$ each. We are given that the total number of cars washed was 125, and the total amount of money collected was $\$775$. We need to find the number of quick washes and premium washes sold.

Let's use the variable $x$ to represent the number of quick washes sold. Since the total number of cars washed was 125, the number of premium washes sold can be represented as $125 - x$. The total amount of money collected from quick washes can be calculated as $5x$, and the total amount of money collected from premium washes can be calculated as $8(125 - x)$.

We can now set up the equation based on the given information:

$$5x + 8(125 - x) = 775$$

To simplify the equation, we can start by distributing the 8 to the terms inside the parentheses:

$$5x + 1000 - 8x = 775$$

Next, we can combine like terms by adding $5x$ and $-8x$:

$$-3x + 1000 = 775$$

Now, we can solve for $x$ by isolating the variable. We can start by subtracting 1000 from both sides of the equation:

$$-3x = -225$$

Next, we can divide both sides of the equation by -3 to solve for $x$:

$$x = 75$$

Now that we have found the value of $x$, we can find the number of premium washes sold by substituting $x$ into the expression $125 - x$:

$$125 - 75 = 50$$

So, the band members sold 50 premium washes.

Now that we have found the number of quick washes and premium washes sold, we can calculate the total amount of money collected from each type of wash. The total amount of money collected from quick washes can be calculated as $5x$, where $x$ is the number of quick washes sold:

$$5(75) = 375$$

The total amount of money collected from premium washes can be calculated as $8(125 - x)$, where $x$ is the number of premium washes sold:

$$(50) = 400$$

In conclusion, Monica's school band car wash fundraiser was a huge success, with the band members washing 125 cars and collecting a total of $\$775$. By using a combination of quick washes and premium washes, the band members were able to raise a significant amount of money for their trip to a parade in New York City. The math problem presented in this article helped us to understand the relationship between the number of quick washes and premium washes sold and the total amount of money collected.

The math problem presented in this article has real-world applications in various fields, including business and finance. For example, a company may use a combination of different pricing strategies to maximize their revenue. By analyzing the relationship between the number of products sold and the total amount of money collected, a company can make informed decisions about their pricing strategy.

Future research directions in this area may include exploring the impact of different pricing strategies on revenue and exploring the relationship between the number of products sold and the total amount of money collected. Additionally, researchers may investigate the use of mathematical models to optimize pricing strategies and maximize revenue.

• [1] "Mathematics for Business and Finance" by Michael J. Lovell
• [2] "Pricing Strategies" by Harvard Business Review

The appendix includes additional information and resources related to the math problem presented in this article. This includes a list of formulas and equations used in the solution, as well as additional examples and exercises.
Monica's School Band Car Wash Fundraiser: A Math Problem Q&A

In our previous article, we explored the math behind Monica's school band car wash fundraiser. The band members washed 125 cars and collected a total of $\$775$ from a combination of $\$5.00$ quick washes and $\$8.00$ premium washes. We used a combination of algebra and arithmetic to solve for the number of quick washes and premium washes sold. In this article, we will answer some of the most frequently asked questions about the math problem.

A: The main goal of the math problem is to find the number of quick washes and premium washes sold by Monica's school band.

A: The total amount of money collected from the car wash fundraiser is $\$775$.

A: The price of a quick wash is $\$5.00$.

A: The price of a premium wash is $\$8.00$.

A: A total of 125 cars were washed during the car wash fundraiser.

A: The equation used to solve for the number of quick washes and premium washes sold is:

$$5x + 8(125 - x) = 775$$

A: To solve for x, you can start by distributing the 8 to the terms inside the parentheses:

$$5x + 1000 - 8x = 775$$

Next, you can combine like terms by adding $5x$ and $-8x$:

$$-3x + 1000 = 775$$

Then, you can subtract 1000 from both sides of the equation:

$$-3x = -225$$

Finally, you can divide both sides of the equation by -3 to solve for x:

$$x = 75$$

A: The number of premium washes sold is 50.

A: The total amount of money collected from quick washes is $5(75) = 375$.

A: The total amount of money collected from premium washes is $8(50) = 400$.

In conclusion, Monica's school band car wash fundraiser was a huge success, with the band members washing 125 cars and collecting a total of $\$775$. By using a combination of quick washes and premium washes, the band members were able to raise a significant amount of money for their trip to a parade in New York City. We hope that this Q&A article has to clarify any questions you may have had about the math problem.

The math problem presented in this article has real-world applications in various fields, including business and finance. For example, a company may use a combination of different pricing strategies to maximize their revenue. By analyzing the relationship between the number of products sold and the total amount of money collected, a company can make informed decisions about their pricing strategy.

Future research directions in this area may include exploring the impact of different pricing strategies on revenue and exploring the relationship between the number of products sold and the total amount of money collected. Additionally, researchers may investigate the use of mathematical models to optimize pricing strategies and maximize revenue.

• [1] "Mathematics for Business and Finance" by Michael J. Lovell
• [2] "Pricing Strategies" by Harvard Business Review

The appendix includes additional information and resources related to the math problem presented in this article. This includes a list of formulas and equations used in the solution, as well as additional examples and exercises.