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Chapter 7: Problem 21

Write the percent proportion. \(10 \%\) of 120 trees is 12 trees.

Short Answer

Expert verified
10% of 120 trees is 12 trees.

Step by step solution

01

- Identify the Percent and Whole

In the problem, the percent given is 10% and the whole number of trees is 120.
02

- Express the Percent as a Fraction

Write the percent as a fraction. Here, 10% can be written as \(\frac{10}{100}\).
03

- Set Up the Proportion

The proportion compares the part (12 trees) to the whole (120 trees) using the percent fraction. Set up the equation \(\frac{10}{100} = \frac{x}{120}\) where \(x\) is the number of trees.
04

- Solve the Proportion

Cross-multiply to solve for \(x\). This gives \(10 \cdot 120 = 100 \cdot x\), which simplifies to \(1200 = 100x\).
05

- Determine the Value of \(x\)

Divide both sides of the equation by 100 to isolate \(x\): \(x = \frac{1200}{100}\). Thus, \(x = 12\).

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Key Concepts

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

Fraction
A fraction represents a part of a whole. It is composed of a numerator and a denominator. In the context of our problem, we turned 10% into a fraction. The standard way to write a percent as a fraction is to put the percentage number over 100. For instance, 10% becomes \(\frac{10}{100}\). This fraction shows that 10 is the part we're interested in out of a total of 100.
Cross-Multiplication
Cross-multiplication is a method used to solve proportions, which are equations that state two ratios are equivalent. In our exercise, we set up the proportion \(\frac{10}{100} = \frac{x}{120}\). Next, we cross-multiply to find the value of x. That means we multiply the numerator of one fraction by the denominator of the other fraction: \[10 \times 120 = 100 \times x\]. The result of cross-multiplying gives us a new equation which we can solve to find our unknown value.
Percentages
Percentages are a way of expressing a number as a fraction of 100. They are useful for comparing proportions. In our problem, we need to find 10% of 120 trees. To do this, we convert the percentage to a fraction, making it easier to set up a proportion, which we then solve. Working with percentages often involves similar conversions and calculations.
Proportional Relationships
Proportional relationships involve two quantities that scale in direct proportion to each other. This means that, as one quantity changes, the other changes at the same rate. In our example, the relationship between the number of trees (12 trees) and the total number of trees (120 trees) can be described proportionally using the percentage 10%. By setting up the equation \(\frac{10}{100} = \frac{12}{120}\), we can see how the quantities are related.

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Most popular questions from this chapter

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.)

Is the number 0.052 less than or greater than \(50 \% ?\)

The maximum recommended heart rate (in beats per minute) is given by 220 minus a person's age. For acrobic activity, it is recommended that individuals exercise at \(60 \%-85 \%\) of their maximum recommended heart rate. This is called the aerobic range. a. Find the maximum recommended heart rate for a 42 -year-old. b. Find the aerobic range for a 42 -year-old.

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?

The amount of 8000 dollar is invested at \(4 \%\) for 3 years. a. Compute the ending balance if the bank calculates simple interese? b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest? (TABLE CAN NOT COPY)
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