The Total Volume Of One Bottle Of Shampoo And One Bottle Of Conditioner Was 845 Milliliters. When Marco Washed His Hair, He Used $\frac{2}{35}$ Of The Shampoo And $\frac{4}{45}$ Of The Conditioner, A Total Of 64 Milliliters.What Are

Introduction

In the world of mathematics, problems often arise in the most unexpected ways. In this case, we are presented with a scenario where Marco uses a portion of his shampoo and conditioner to wash his hair, but the total volume of the products used is less than expected. Our task is to determine the total volume of the shampoo and conditioner used by Marco.

The Problem

The total volume of one bottle of shampoo and one bottle of conditioner was 845 milliliters. When Marco washed his hair, he used $\frac{2}{35}$ of the shampoo and $\frac{4}{45}$ of the conditioner, a total of 64 milliliters.

Let's Break it Down

To solve this problem, we need to find the total volume of the shampoo and conditioner used by Marco. We can start by setting up an equation to represent the situation.

Let $x$ be the volume of the shampoo used by Marco, and let $y$ be the volume of the conditioner used by Marco. We know that the total volume of the shampoo and conditioner used is 64 milliliters, so we can write the equation:

$$x + y = 64$$

We also know that the volume of the shampoo used is $\frac{2}{35}$ of the total volume of the shampoo, and the volume of the conditioner used is $\frac{4}{45}$ of the total volume of the conditioner. We can write the equations:

$$x = \frac{2}{35} \times 845$$

$$y = \frac{4}{45} \times 845$$

Solving the Equations

Now that we have the equations, we can solve for $x$ and $y$.

First, let's solve for $x$:

$$x = \frac{2}{35} \times 845$$

$$x = 48.5$$

Next, let's solve for $y$:

$$y = \frac{4}{45} \times 845$$

$$y = 75.11$$

The Final Answer

Now that we have the values of $x$ and $y$, we can find the total volume of the shampoo and conditioner used by Marco.

The total volume of the shampoo used is 48.5 milliliters, and the total volume of the conditioner used is 75.11 milliliters. Therefore, the total volume of the shampoo and conditioner used by Marco is:

$$48.5 + 75.11 = 123.61$$

Conclusion

In this problem, we were presented with a scenario where Marco used a portion of his shampoo and conditioner to wash his hair, but the total volume of the products used is less than expected. We were able to solve for the total volume of the shampoo and conditioner used by Marco by setting up equations and solving for the unknowns.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Fractions: We used fractions to represent the portion of the shampoo and conditioner used by Marco.
• Equations: We set up equations to represent the situation and solve for the unknowns.
• Algebra: We used algebraic techniques to solve for the unknowns.

Real-World Applications

This problem has real-world applications in the following areas:

• Personal care: The problem is relevant to personal care products such as shampoo and conditioner.
• Mathematics in everyday life: The problem demonstrates how mathematics is used in everyday life to solve real-world problems.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

• Read the problem carefully: Make sure you understand the problem and what is being asked.
• Set up equations: Use equations to represent the situation and solve for the unknowns.
• Use algebraic techniques: Use algebraic techniques to solve for the unknowns.

Conclusion

Q&A: The Mysterious Case of the Missing Shampoo and Conditioner

Q: What is the total volume of one bottle of shampoo and one bottle of conditioner?

A: The total volume of one bottle of shampoo and one bottle of conditioner is 845 milliliters.

Q: What portion of the shampoo and conditioner did Marco use?

A: Marco used $\frac{2}{35}$ of the shampoo and $\frac{4}{45}$ of the conditioner.

Q: What is the total volume of the shampoo and conditioner used by Marco?

A: The total volume of the shampoo and conditioner used by Marco is 64 milliliters.

Q: How did you solve for the total volume of the shampoo and conditioner used by Marco?

A: We set up equations to represent the situation and solved for the unknowns. We used the equations:

$$x + y = 64$$

$$x = \frac{2}{35} \times 845$$

$$y = \frac{4}{45} \times 845$$

Q: What are the values of x and y?

A: The value of x is 48.5 milliliters, and the value of y is 75.11 milliliters.

Q: What is the total volume of the shampoo and conditioner used by Marco?

A: The total volume of the shampoo and conditioner used by Marco is 123.61 milliliters.

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

A: The mathematical concepts involved in solving this problem are:

• Fractions: We used fractions to represent the portion of the shampoo and conditioner used by Marco.
• Equations: We set up equations to represent the situation and solve for the unknowns.
• Algebra: We used algebraic techniques to solve for the unknowns.

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

A: This problem has real-world applications in the following areas:

• Personal care: The problem is relevant to personal care products such as shampoo and conditioner.
• Mathematics in everyday life: The problem demonstrates how mathematics is used in everyday life to solve real-world problems.

Q: What tips and tricks can you offer to help solve this problem?

A: Here are some tips and tricks to help you solve this problem:

• Read the problem carefully: Make sure you understand the problem and what is being asked.
• Set up equations: Use equations to represent the situation and solve for the unknowns.
• Use algebraic techniques: Use algebraic techniques to solve for the unknowns.

Conclusion

In conclusion, this problem demonstrates how mathematics is used in everyday life to solve real-world problems. By setting up equations and solving for the unknowns, we were able to find the total volume of the shampoo and conditioner used by Marco. This problem has real-world applications in the areas of personal care and mathematics in everyday life.