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Chapter 6: Problem 26

Translate to a proportion. Do not solve. $$ 80 \% \text { of what is } 96 ? $$

Short Answer

Expert verified
\( \frac{80}{100} = \frac{96}{x} \)

Step by step solution

01

Identify the Components

Identify the parts of the question. The percentage is 80%, the known value is 96, and the unknown value is what we need to find.
02

Set up the Proportion

We need to express the statement '80% of what is 96' as a proportion. Let the unknown value be represented by the variable x.
03

Write the Proportion

In a proportion, the part out of the whole is set equal to another part out of a whole. Here, we can write: \[ \frac{80}{100} = \frac{96}{x} \]

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Key Concepts

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

Percentage
Percentages are a way to express numbers as parts of a whole. The 'whole' is always out of 100.
For example, 80% means 80 out of 100.
In our exercise, the 80% shows how much of the 'whole' we are dealing with.
When converting percentages to decimals, you divide the percentage by 100.
  • 80% becomes 0.80
  • 50% becomes 0.50
  • 25% becomes 0.25
Understanding this concept is crucial for setting up proportion problems.
Unknown Variable
In mathematics, an unknown variable is represented by symbols like x, y, or z.
These symbols stand in for numbers we don't yet know. In our problem,
we need to find the value 'what' or 'x' in the statement '80% of what is 96'.
Here, x represents the unknown number that 80% of will result in 96.
When setting up equations or proportions involving unknown variables, it's essential to correctly identify and isolate the variable.
This helps simplify the equation and makes it easier to solve later.
Mathematical Proportion
A proportion is an equation that states two ratios are equal. Ratios compare two numbers or quantities.
In our exercise, the problem is translated into a proportion: \[\frac{80}{100} = \frac{96}{x}\] Here, we are comparing the ratio of 80% to 100% with the ratio of 96 to the unknown variable x. Setting up proportions helps in solving many types of problems, especially those involving percentages.
Always remember to solve for the unknown variable by cross-multiplying and dividing if needed, though in this exercise we are not solving but just setting it up.

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