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Chapter 6: Problem 27

Translate to an equation and solve. 56.32 is \(64 \%\) of what?

Short Answer

Expert verified
88

Step by step solution

01

- Understand the problem

We need to find a number such that 64% of it equals 56.32.
02

- Set up the equation

Let the unknown number be represented by the variable x. The equation can be written as \[0.64x = 56.32\]
03

- Solve for x

To solve for x, divide both sides of the equation by 0.64:\[ x = \frac{56.32}{0.64} \]
04

- Calculate the value

Perform the division to find x:\[ x = 88 \]

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Key Concepts

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

Equation Solving
Solving equations is a key skill in mathematics. In this exercise, we had to find an unknown number based on a given percentage. The steps to solving an equation generally include:
  • Understanding the problem
  • Setting up the equation
  • Solving for the unknown
In this problem, we set up our equation as \[0.64x = 56.32\] and then solved for the unknown number by isolating the variable x.
Percentages
Percentages are used to express proportions and are a common way to describe parts of a whole. They are always based on the number 100. For example, 64% means 64 out of 100. To find what number 56.32 represents 64% of, we need to translate this percentage into a decimail when setting up our equation. This meant converting \64\% to \0.64\ and using it in our equation: \[0.64x = 56.32\].
Remember, to convert percentages to decimals, you divide by 100. So \64\% becomes \0.64\.
Mathematical Translation
Mathematical translation involves converting words into mathematical expressions or equations. This exercise required translating the phrase '56.32 is 64% of what?' into a solvable equation. Here's how we approached it:
  • The word 'is' translates to the equal sign \(=\).
  • '64% of' means we multiply 0.64 by the unknown number.
  • 'What' is our unknown variable, x.
This gives us the equation: \[0.64x = 56.32\]. Translating word problems into equations is a powerful tool, making it possible to apply algebraic methods to find solutions.

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