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Chapter 7: Problem 28

Write the percent equation. Then solve for the unknown base. 72 is \(30 \%\) of what number?

Short Answer

Expert verified
The unknown base is 240.

Step by step solution

01

- Write the Percent Equation

The percent equation can be written as: percent 脳 base = amount In this case, the amount is 72 and the percent is 30%.
02

- Set up the Equation

Substitute the given values into the percent equation: 0.30 脳 base = 72 Note: Convert the percentage to a decimal by dividing by 100.
03

- Solve for the Base

To isolate the base, divide both sides of the equation by 0.30: base = \(\frac{72}{0.30}\)
04

- Calculate the Base

Perform the division to find the base: base = 240

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Key Concepts

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

Percent Problems
Let's start with understanding percent problems. Percent problems often require you to find the percentage, the base (the original number), or the amount (the result after applying the percentage). In our exercise, we need to find the base. This type of problem is common in everyday scenarios, like finding out discounts, interest rates, or comparing quantities. To tackle these problems easily, remember the percent equation: percent 脳 base = amount. This equation shows the relationship between the percentage, the base, and the amount.
Solving for Unknowns
Solving for unknowns is a critical math skill. In our exercise, the unknown is the base, which we don't know yet. First, we write down the percent equation: 0.30 脳 base = 72. Here, 0.30 (30% as a decimal) and 72 (the amount) are known. To isolate the base, which is our unknown, we need to perform some basic algebra. Divide both sides of the equation by 0.30 to get base = \(\frac{72}{0.30}\). Solving for unknowns like this helps us transform an equation step by step until we find the value of the unknown.
Basic Algebra
Basic algebra allows us to manipulate equations and find unknowns. In the exercise, we used division, a fundamental algebraic operation, to isolate the base. First, substitute the given values into the percent equation: 0.30 脳 base = 72. Then, divide both sides by 0.30 to isolate the base: base = \(\frac{72}{0.30}\). This step-by-step transformation is at the heart of algebra. By mastering these simple operations, you can solve complex problems systematically.
Mathematical Operations
Understanding mathematical operations is key to solving percent problems. In this exercise, we primarily used multiplication and division. First, we converted 30% to a decimal by dividing by 100, resulting in 0.30. Then, we multiplied this by the base to set up our equation: 0.30 脳 base = 72. To solve for the base, we divided both sides by 0.30: base = \(\frac{72}{0.30}\). Performing these operations accurately is crucial. Practicing helps in making these steps more intuitive and quick to execute.

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Most popular questions from this chapter

Solve the problem using a percent equation. \(350 \%\) of what number is \(2100 ?\)

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 \(15 \%\) tip on a luncheon bill of \(\$ 12.00\)

Solve the problem using a percent proportion. \(0.8 \%\) of what number is \(192 ?\)

The point \(P\) lies in the first quadrant on the graph of the line \(y=7-3 x\). From the point \(P\), perpendiculars are drawn to both the \(x\) -axis and the \(y\) -axis. What is the largest possible area for the rectangle thus formed?

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 \(\$ 57.65\) (Hint: Round up to \$58 first.)
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