/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 Translate to an equation and sol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 25

Translate to an equation and solve. \(35 \%\) of what number is \(77 ?\)

Short Answer

Expert verified
Answer: The number is 220.

Step by step solution

01

Convert percentage to decimal

We need to convert \(35 \%\) to its decimal form. To do this, divide 35 by 100. \(35 \% = \frac{35}{100} = 0.35\)
02

Set up an equation

Let the number we are looking for be represented by \(x\). We know that \(35 \%\) of this number is \(77\), so we can represent this relationship with the following equation: \(0.35 \times x = 77\)
03

Solve the equation

To isolate \(x\), we need to divide both sides by \(0.35\): \(x = \frac{77}{0.35}\) Now, calculate the value of \(x\): \(x = 220\) The number we were looking for is \(220\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Percentages
A percentage is a way to express a number as a part of a whole. Specifically, it is a fraction with a denominator of 100. For example, 35% means 35 out of every 100. This is a very common way to compare quantities and is particularly useful in everyday life.

Percentages help us understand proportions and ratios. They are used in setting discounts, calculating interest rates, and analyzing data in various fields.
  • To find a percentage of a number, you multiply the number by the percentage in decimal form.
  • Conversely, to find what percentage one number is of another, you divide the part by the whole and multiply by 100.

Understanding how to work with percentages creates a strong foundation for solving many practical problems.
Solving Equations
An equation is a mathematical statement that asserts the equality of two expressions. In the case of finding the number in our problem, we use a simple equation to isolate the variable. Here, the equation is a tool to express the relationship given in a word problem more clearly.

When solving equations, the goal is to find the value of the unknown variable. To do this, you will perform operations that simplify the equation, ultimately isolating the variable on one side.
  • For example, if you start with an equation like \(0.35 \times x = 77\), you need to perform the reverse operation to isolate \(x\), which involves dividing both sides by 0.35.
  • Solving equations is a fundamental skill in mathematics, allowing you to apply logical steps to reach a solution.

Practicing with different types of equations strengthens your problem-solving capabilities.
Converting Percentages to Decimals
To work effectively with percentages in mathematical equations, converting them to decimals is essential. This conversion simplifies calculations and helps when setting up and solving equations.

Converting a percentage to a decimal is straightforward:
  • Start by dividing the percentage by 100. For example, 35% becomes \(\frac{35}{100} = 0.35\).
  • This conversion is important because it allows you to use the percentage directly in multiplication and division within equations.

Remember, moving the decimal point two places to the left also transforms the percentage into a decimal. This method can be particularly handy in mental math.
Being comfortable with this conversion makes dealing with percentages in equations much easier, ensuring accurate results.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain the mistake, then solve the problem correctly. What percent of 60 is \(15 ?\) $$ \begin{aligned} 60 p &=15 \\ \frac{60 p}{60} &=\frac{15}{60} \\ p &=0.25 \end{aligned} $$

Solve. Hannah purchased a curio stand discounted \(35 \%\). If the price after the discount was \(\$ 246.68\), what was the initial price?

The following table contains the Jones family's net monthly income and expenses. $$\begin{aligned} &2\\\ &\begin{array}{l|l} \text { Income } & \text { Expenses } \\ \hline \text { Mr. Jones: } \$ 2252.70 & \text { Mortgage: } \$ 1680 \\ \hline \text { Mrs. Jones: } \$ 2597.30 & \text { Car Loan } 1: \$ 380 \\ \hline & \text { Car Loan } 2: \$ 465 \\ \hline & \text { Credit Card Payments: } \$ 220 \\ \hline & \text { Utilities: } \$ 485 \\ \hline & \text { Groceries: } \$ 450 \\ \hline \end{array} \end{aligned}$$ a. Complete the following table with the percent of the total monthly income that each expense represents. (Round each percent to one decimal place.) $$\begin{array}{l|c|c|c|c|c|c} & \text { Mortgage } & \text { Car loan 1 } & \text { Car loan 2 } & \begin{array}{c} \text { Credit card } \\ \text { payments } \end{array} & \text { Utilities } & \text { Groceries } \\ \hline \begin{array}{l} \text { Percent of total } \\ \text { monthly income } \end{array} & & & & & & \end{array}$$ b. What is the total percent of the family's income paid toward expenses? c. What percent of the family's income is left after all expenses are paid? d. Draw a circle graph showing the percent of the total monthly income that each expense represents, along with the percent remaining after all expenses are paid. (Circle can't copy)

Write each percent as a decimal number. $$1.65 \%$$

Solve. Denzel received a \(9 \%\) raise. His new salary is \(\$ 39,828.60 .\) What was his former salary?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.