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Chapter 6: Problem 114

Translate and solve. What percent of 260 is 78?

Short Answer

Expert verified
78 is 30% of 260.

Step by step solution

01

Set up the Equation

To find what percent of 260 is 78, set up the equation \[ \frac{78}{260} = x \] where \(x\) represents the percentage in decimal form.
02

Solve for x

Divide 78 by 260 to solve for \(x\): \[ x = \frac{78}{260} \] Performing the calculation gives you \[ x \approx 0.3 \]
03

Convert to a Percentage

To convert the decimal to a percentage, multiply by 100. \[ x \times 100 = 0.3 \times 100 = 30 \] Therefore, 78 is 30% of 260.

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Key Concepts

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

Percentages
Percentages are a way to express a number as a fraction of 100. They are used to compare proportions. For instance, if we say that 50% of students passed an exam, it means 50 out of every 100 students passed. To solve percentage problems, you often convert fractions and decimals, and vice versa. The basic formula for finding the percentage is: \[ \text{Percentage} = \frac{\text{part}}{\text{whole}} \times 100 \] In our exercise, we need to find what percent 78 is of 260. We do this by setting up the equation as a fraction and then converting it to a decimal before finally multiplying by 100 to get the percentage.
Equations
Equations are mathematical statements that show the equality between two expressions. They are essential for solving many types of math problems, including percentages. To solve for a variable in an equation, you typically perform operations that isolate the variable on one side of the equation. In our problem, the equation \[ \frac{78}{260} = x \] helps us to find the decimal form of the percentage. By isolating \( x \), we determine how much part of the whole 260 is represented by 78.
Fractions
Fractions show a part of a whole and are composed of a numerator (the top number) and a denominator (the bottom number). They are crucial in various calculations, including finding percentages. To find what percent of 260 is 78, we set up a fraction: \[ \frac{78}{260} \] This fraction represents the part (78) over the whole (260). Simplifying fractions whenever possible makes calculations easier but is not always necessary for solving a percentage problem, especially if a calculator or software is used.
Decimal Conversion
Decimal conversion is the process of converting fractions to decimal form, making them easier to work with in further calculations. After you have a fraction like \( \frac{78}{260} \), you can convert it to a decimal by performing the division: \[ \frac{78}{260} \] When you calculate this, you get: \[ x \approx 0.3 \] This decimal can then be converted to a percentage by multiplying by 100: \[ 0.3 \times 100 = 30 \] Hence, 78 is 30% of 260.

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Most popular questions from this chapter

In the following exercises, find (a) the amount of the mark-up (b) the list price Manny paid \(\$ 0.80\) a pound for apples. He added 60\(\%\) mark-up before selling them at his produce stand. What price did he charge for the apples?

In the following exercises, solve. Jorge got a raise in his hourly pay, from \(\$ 19.00\) to \(\$ 19.76 .\) Find the percent increase.

Solve the applications of percents. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

In the following exercises, find the sale price. Aya bought a pair of shoes that was on sale for \(\$ 30\) off. The original price of the shoes was \(\$ 75 .\)

In the following exercises, convert each fraction to a percent. (Round to 3 decimal places if needed.) $$ \frac{11}{12} $$
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