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Chapter 7: Problem 5

Find the answer mentally. 20 is \(50 \%\) of what number?

Short Answer

Expert verified
40

Step by step solution

01

Understand the Problem

To solve the problem, it's necessary to determine a number for which 20 is 50% of that number. Mathematically, this can be represented as finding 'x' such that 0.5x = 20.
02

Set Up the Equation

Write the equation based on the given information. The problem states that 20 is 50% of a number. Therefore, we can write the equation as \[ 0.5x = 20 \].
03

Solve the Equation

To find the number 'x', divide both sides of the equation by 0.5:\[ x = \frac{20}{0.5} \]. This simplifies to \[ x = 40 \].

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Key Concepts

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

Mental Math
Mental math allows us to solve problems in our heads without using calculators or paper. It is a useful skill in dealing with simple arithmetic and enhances our cognitive abilities. To solve: '20 is 50% of what number?' mentally, follow these steps:
Understand that 50% means half. This can be translated to a simple fraction: \(\frac{1}{2}\)
If 20 is half of a number, you need to think of what number times \(\frac{1}{2}\) equals 20.
To find the answer, imagine doubling 20 since it's half of the original number, arriving at 40.
Regular mental exercises like these improve your math skills and make everyday tasks easier.
Equation Solving
Solving equations involves finding the value of an unknown variable that makes the equation true. In our problem: '20 is 50% of what number?' we can set up an equation to find the unknown number.
Steps to solve: First, translate the word problem into a mathematical equation: \(0.5x = 20\).
Here, 'x' represents the number we're looking for.
Next, isolate the variable 'x' by performing the same operation on both sides of the equation: \(x = \frac{20}{0.5}\)
Finally, solve the division to find 'x': \(x = 40\). By following these steps, we see that '20 is 50% of 40'.
Fractions
Fractions represent parts of a whole and are useful for expressing proportions and percentages. In our exercise: '20 is 50% of what number?' we deal with the fraction \(\frac{1}{2}\), which is equivalent to 50%.
Understanding fractions helps us translate between percentages and whole numbers. You can practice converting fractions and percentages in both directions.
For example, \(50\text{\%} = \frac{1}{2}\)
To find a number when given a fraction of it, divide the known part by the fraction. In our case, it's \(\frac{20}{0.5} = 40\)
Knowing these relationships makes working with percentages much simpler and is a critical math skill.

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Most popular questions from this chapter

Brian has been saving money to buy a 61-in. Samsung Projection HDTV. He has saved \(\$ 1440\) so far, but this is only \(60 \%\) of the total cost of the television. What is the total cost?

Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 9,000$$ Annual Interest Rate $$8 \%$$ Time, Years $$2$$ Compounded Monthly Total Amount __________

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{13}{15}$$

Find the total amount in an account for an investment subject to the following conditions. Principal \$ 4,000 Annual Interest Rate $$3 \%$$ Time, Years $$3$$ Compounded Semiannually Total Amount __________

Convert the fraction to a percent. $$2 \frac{1}{8}$$
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