Chapter 8: Problem 30
Translate to an equation and solve. 645 is \(12.9 \%\) of what number?
Short Answer
Expert verified
Answer: The original number is approximately 4,992.25.
Step by step solution
01
Set up the equation.
The given information can be written in the form of the equation,
$$ 645 = 12.9\% \times X $$
Where X is the original number we want to find.
02
Convert the percentage to a decimal.
In order to solve the equation, we should first convert the percentage to a decimal number. To do this, divide the percentage by 100:
$$ 12.9\% \ = \frac{12.9}{100}=0.129 $$
03
Substitute the decimal value into the equation.
Now, we substitute the decimal value (0.129) into the equation from Step 1:
$$ 645 = 0.129 \times X $$
04
Solve for X.
To find the value of X, we divide both sides of the equation by 0.129:
$$ X = \frac{645}{0.129} $$
Now, perform the division:
$$ X \approx 4,992.25 $$
05
Write the final answer.
Therefore, 645 is approximately 12.9% of the original number 4,992.25.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Translating Word Problems to Equations
Translating word problems into equations can sometimes feel like translating another language. It is all about interpreting the words and numbers into a mathematical statement. In the example given, "645 is 12.9% of what number?", the task is to represent all the elements of the sentence mathematically.
If we break it down:
If we break it down:
- "645 is" becomes "645 = " indicating what one side of the equation will equal.
- "12.9% of" means that 12.9% will be applied on some number, commonly represented as multiplication "\( \times \)" with a variable, typically "X".
- "What number?" signifies that this is the unknown quantity, so we use a variable to denote it. Here, we utilize "X".
Solving Equations
Solving equations is a foundational skill in mathematics, enabling you to find the unknown value represented by variables. For the equation \( 645 = 0.129 \times X \), derived from the translation of a word problem, the goal is to isolate "X."
- First, understand that \( 0.129 \times X \) means "multiplying X by 0.129". So, to reverse this multiplication, we perform division on both sides of the equation.
- Divide 645 by 0.129 to isolate X. In equation form, this looks like \( X = \frac{645}{0.129} \).
- After calculating, you find that \( X \approx 4,992.25 \). This gives us the estimated value of "X."
Decimal Conversion
Understanding decimal conversion is essential, especially when working with percentages. To solve equations involving percentages, converting these percentages into decimal form is necessary. The process is simple yet critical:
- To convert a percentage to a decimal, divide by 100 because "percent" means "per hundred."
- For example, convert 12.9\% to a decimal: \( \frac{12.9}{100} = 0.129 \).
- Use this decimal number in your calculations, making equations easier to manage and solve, such as in the equation \( 645 = 0.129 \times X \).