Question

Translate to an equation and solve. \(60 \%\) of an 800 -milliliter mixture is HCl (hydrochloric acid). How many milliliters of the solution are HCl?

Short answer

Answer: 480 mL

Step-by-step solution

Translate the problem into an equation

Let x be the amount of HCl in milliliters. Write the equation as follows: x = 60% * 800 mL

Convert the percentage to a decimal

We need to convert the percentage to a decimal, so 60% becomes 0.6: x = 0.6 * 800 mL

Calculate the amount of HCl

Now, we can multiply 0.6 by 800 to find the amount of HCl in the mixture: x = 480 mL So, there are 480 milliliters of HCl in the 800-milliliter mixture.

Key concepts

Percentage Calculations

Understanding percentages is key when dealing with word problems like the one presented. A percentage represents a part out of 100, indicating how a value compares to a whole.
Here, we have 60%, meaning that 60 out of every 100 parts of the mixture is HCl. To find out how much HCl is in 800 mL, we need to convert this percentage into a decimal. Converting percentages to decimals is a simple process:

• Take the percentage (60%) and remove the percentage symbol.
• Then divide the number by 100.
• So, 60% becomes 0.6.

Once we've converted the percentage into a decimal, we can use this to find the desired part of the whole. When we multiply 0.6 (the decimal version of 60%) by 800 mL, it gives us the proportion of hydrochloric acid in milliliters.

Translation of Word Problems into Equations

Translating word problems into equations is an essential skill that makes problem-solving easier. In this process, we turn a problem expressed in words into a mathematical statement.
First, identify the key information: here, it's that 60% of the 800 mL mixture is HCl. We introduce a variable, such as \( x \), to represent the unknown quantity we want to find. In this case, \( x \) signifies the amount of HCl.
The problem tells us 60% of 800 mL, which translates to the equation:

• \( x = 60\% \times 800 \text{ mL} \)

Creating equations from word problems involves recognizing the relationship between the quantities given and turning them into a form that is solvable using basic arithmetic.

Basic Arithmetic Operations

Basic arithmetic operations like multiplication, addition, and division are the building blocks of solving equations. In our example, we need to find 60% of 800, which requires multiplication:
We have already converted 60% to a decimal as 0.6. The next step involves multiplying 0.6 by 800 to compute the amount of HCl in the solution. Performing this calculation directly provides the answer through a straightforward arithmetic operation:

• \( 0.6 \times 800 = 480 \text{ mL} \)

Here, multiplying 0.6 by 800 involves handling both whole numbers and decimals, demonstrating how basic multiplication can be used to solve real-world problems. Understanding these operations ensures accurate and effective problem solving, especially in scenarios involving real-life applications such as percentages and proportions.