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Chapter 6: Problem 27

Translate to a proportion. Do not solve. $$ 65.12 \text { is } 74 \% \text { of what? } $$

Short Answer

Expert verified
Translate to \(\frac{65.12}{x} = \frac{74}{100}\).

Step by step solution

01

Identify the components

Recognize the given values in the problem: 65.12 is the part, 74% is the percentage, and the unknown whole is what we need to find.
02

Set up the proportion format

Write the proportion using the formula \(\frac{part}{whole} = \frac{percentage}{100}\). In this case, \(\frac{65.12}{x} = \frac{74}{100}\).
03

Translate to proportion

Translate the given problem into a proportion: \(\frac{65.12}{x} = \frac{74}{100}\).

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Key Concepts

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

Understanding Percentages
Percentages are a way of expressing a number as a fraction of 100. They tell us how much out of every hundred. For instance, 74% means 74 out of 100.
They are widely used in everyday life and various fields, like finance and statistics.
To convert percentages to decimals, we divide by 100. For example, 74% becomes 0.74 when divided by 100.
Percentages are useful for comparing different quantities on a common scale. This makes it easy to understand and interpret them.
Basics of Algebra
Algebra involves using symbols and letters to represent numbers and quantities.
This branch of mathematics helps us in gaining an understanding of how things change and relate to each other.
In expressions, letters stand for different numbers which we might not know yet. 
For example, in the expression \(x + 2 = 5\), we can find that \(x\) must be 3 because 3 plus 2 equals 5.
Using algebra, we can write complex problems in simpler forms and solve them step by step.
This makes it easier to find unknown values (like the whole amount in proportion problems), through a systematic approach.
Mathematical Translation
Mathematical translation involves converting word problems into mathematical expressions or equations.
This process helps us to understand and solve the problem accurately.
For instance, in the problem '65.12 is 74% of what?', we can identify three key components:
  • 65.12 (the part or portion)
  • 74% (the percentage)
  • The unknown whole we need to find
We then translate this information into a proportion using the formula \[ \frac{part}{whole} = \frac{percentage}{100} \].
Here, we set it up as \[ \frac{65.12}{x} = \frac{74}{100} \]. By translating the problem into this mathematical form, we can more easily solve for the unknown value through algebraic steps.

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Most popular questions from this chapter

The Mississippi River, which extends from its source at Lake Itasca in Minnesota to the Gulf of Mexico, is 2348 mi long. Approximately \(77 \%\) of the river is navigable. How many miles of the river are navigable?

Multiply and simplify. $$ \frac{4}{15} \times \frac{3}{20} $$

Solve. $$ 0.64 \cdot x=170 $$

Convert to decimal notation. \(\frac{18}{102}\)

Solve. Kansas Sales Tax. The sales tax rate in Kansas is \(6.5 \% .\) How much sales tax would be charged on a fireplace screen with doors that costs \(\$ 239 ?\)
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