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Chapter 7: Problem 42

Solve the percent problems with an unknown base. 9.5 is \(200 \%\) of what number?

Short Answer

Expert verified
The base number is 4.75.

Step by step solution

01

Understand the problem

You need to find the unknown base when you know that 9.5 is equivalent to 200% of that base number.
02

Convert percentage to decimal

Convert the percentage into a decimal to make calculations easier. Remember that 200% is the same as 200 divided by 100, which equals 2. So, 200% = 2 in decimal form.
03

Set up the equation

Use the formula: o the percentage (in decimal form) 脳 base = amountSo, 2 脳 base = 9.5.
04

Solve for the base

To find the base, divide 9.5 by 2:\(\frac{9.5}{2} = 4.75\)Therefore, the base number is 4.75.

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Key Concepts

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

Unknown Base
When working with percent problems, one common task is to find the 'unknown base.' This means you are given a percentage and the result, and you need to figure out the original number before the percentage was applied. In our example, we know that 9.5 is 200% of some number, and we need to find that number.

The unknown base is the value we are trying to determine. It's like trying to figure out the original amount of money you started with before it was doubled (if 200% means doubled). The key is to set up the right equation and convert the percentage to a usable form like a decimal or fraction.
Convert Percentage
One of the crucial steps in solving percent problems is converting the percentage into a more manageable form, typically a decimal.

Here鈥檚 how you can convert a percentage to a decimal:
  • First, understand that 'percent' means 'per hundred.'
  • To convert any percentage to a decimal, divide by 100.
In our example, we had 200%. To convert 200% to a decimal, we divide 200 by 100:

\[ \frac{200}{100} = 2 \]

Now, we have the more manageable decimal form of the percentage, which is 2. This is much easier to work with in equations.
Solving Equations
After converting the percentage to a decimal, we can set up a simple equation to solve for the unknown base.

Let鈥檚 break down the steps:
  • We know that the decimal form of 200% is 2.
  • We also know that this 2, when multiplied by our unknown base, equals 9.5.
So, our equation looks like this:

\[ 2 \times \text{base} = 9.5 \]

To solve for the base, we need to isolate it. We do this by performing the inverse operation of multiplication, which is division. We divide both sides of the equation by 2:

\[ \text{base} = \frac{9.5}{2} \]

Finally, when we compute the division, we find that the base is 4.75. So, 9.5 is 200% of 4.75. This step-by-step approach will help you solve similar percent problems with confidence.

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Most popular questions from this chapter

Forty-four percent of Americans use online travel sites to book hotel or airline reservations. If 400 people need to make airline or hotel reservations, how many would be expected to use online travel sites?

Convert the fraction to a percent. $$\frac{11}{9}$$

In a recent survey, \(38 \%\) of people in the United States say that gas prices have affected the type of vehicle they will buy. In a sample of 500 people who are in the market for a new vehicle, how many would you expect to be influenced by gas prices?

It is customary to leave a \(15-20 \%\) tip for the server in a restaurant. However, when you are at a restaurant in a social setting, you probably do not want to take out a pencil and piece of paper to figure out the tip. It is more socially acceptable to compute the tip mentally. Try this method. Step 1: First, if the bill is not a whole dollar amount, simplify the calculations by rounding the bill to the next-higher whole dollar. Step 2: Take \(10 \%\) of the bill. This is the same as taking one-tenth of the bill. Move the decimal point to the left 1 place. Step 3: If you want to leave a 20\% tip, double the value found in step 2. Step 4: If you want to leave a \(15 \%\) tip, first note that \(15 \%\) is \(5 \%+10 \% .\) Therefore, add one-half of the value found in step 2 to the number in step 2 . Estimate a \(20 \%\) tip on a bill of \(\$ 18.79\)

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{3}{7}$$
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