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Chapter 7: Problem 67

Solve the problem using a percent proportion. \(0.5 \%\) of what number is \(44 ?\)

Short Answer

Expert verified
x = 8800

Step by step solution

01

Understand the Problem

You need to find the number, say it is 'x,' such that 0.5% of x equals 44.
02

Set Up the Proportion

Set up a percent proportion using the formula \[\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}\]. In this problem, the 'part' is 44, the 'percent' is 0.5, and the 'whole' is the unknown number, x. Therefore, the proportion will be: \[\frac{44}{x} = \frac{0.5}{100}\].
03

Solve the Proportion

Cross-multiply to solve for x. \[44 \times 100 = 0.5 \times x\] \[\rightarrow 4400 = 0.5x\].
04

Find x

Solve for x by dividing both sides of the equation by 0.5. \[\frac{4400}{0.5} = x\], Therefore, \x = 8800\.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percent Calculation
Understanding how to calculate percentages is essential for solving many math problems. A percentage represents a fraction of 100. For example, 0.5% means 0.5 out of every 100 units. Calculating percentages involves three main types:
  • Finding the percentage of a number.
  • Finding what number a percentage represents.
  • Finding the whole when given a part and a percentage.
In our problem, we are given 0.5% and need to find the whole number for which 44 is 0.5%.
Cross-Multiplication
Cross-multiplication is a method used in algebra to solve proportions or fractions equal to each other. By cross-multiplying, we eliminate fractions and create a simpler equation to solve. Here's how you do it:
  • Identify the two fractions set equal to each other.
  • Multiply the numerator of the first fraction by the denominator of the second fraction.
  • Multiply the numerator of the second fraction by the denominator of the first fraction.
  • Set the two products equal to each other and solve for the variable.
In our problem, we have the proportion: \frac{44}{x} = \frac{0.5}{100}\. By cross-multiplying, we get: \(44 \times 100 = 0.5 \times x\).
Solving Equations
Solving equations is about finding the value of the unknown that makes the equation true. Here鈥檚 the general process:
  • Isolate the variable on one side of the equation.
  • Perform inverse operations to solve for the variable.
In our example, we arrived at the equation: \(4400 = 0.5x\). To isolate \(x\), we divide both sides of the equation by 0.5, resulting in \(x = \frac{4400}{0.5}\). Finally, we solve the division to get \(x = 8800\).
Basic Algebra
Basic algebra focuses on understanding how to manipulate equations and expressions using variables and constants. Key concepts include:
  • Understanding variables and coefficients.
  • Performing arithmetic operations with variables.
  • Using properties of equality to solve equations.
In our percent proportion problem, we see all these concepts in action. We translated a real-world situation into an equation, used proportional reasoning, cross-multiplication, and algebraic manipulation to find the solution.

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