/*! 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 32 Translate to an equation and sol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 32

Translate to an equation and solve. What is \(35 \frac{1}{4} \%\) of \(1200 ?\)

Short Answer

Expert verified
35.25% of 1200 is 423.

Step by step solution

01

Convert the percentage to a decimal

Percentages are converted to decimals by dividing by 100. So, convert 35.25% to a decimal: \(\frac{35.25}{100} = 0.3525 \)
02

Set up the equation

We need to find what 35.25% of 1200 is. This can be set up as the following equation: \( x = 0.3525 \times 1200 \).
03

Solve the equation

Multiply the decimal obtained in Step 1 by 1200: \( x = 0.3525 \times 1200 \) = \(x = 423 \)

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.

converting percentages to decimals
Understanding how to convert percentages to decimals is essential in solving percentage problems. Percentages represent a fraction of 100. Therefore, to convert a percentage to a decimal, divide by 100. For instance, if we take the percentage 35.25%, we perform the following division:

\( \frac{35.25}{100} = 0.3525 \).

This simple operation transforms the percentage into a decimal, making it easier to handle in mathematical equations.

Let鈥檚 take another example:
If we have 50%, converting to a decimal becomes
\( \frac{50}{100} = 0.50.\).

This is a straightforward step, yet very important for further calculations.
setting up equations
Equations are used to represent real-world problems mathematically. Once we have converted the percentage to a decimal, we can set up an equation to solve the problem. Let鈥檚 use our exercise as an example. We want to find what 35.25% of 1200 is.

First, we converted 35.25% to 0.3525. The phrase '35.25% of 1200' can be translated into the equation: \( x = 0.3525 \times 1200 \).

Here, x represents the value we are looking for.

In general terms, if you want to find out what any percentage (P) of a number (N) is, the equation will be:
\[ x = \frac{P}{100} \times N \]
Remember to always convert the percentage first.
solving multiplication problems
The final step is to solve the equation we鈥檝e set up. In our example, we need to multiply the decimal 0.3525 by 1200.

The equation is:

\( x = 0.3525 \times 1200 \)

We can break down the multiplication step-by-step:

  • First, multiply 0.3525 by 1200 directly.
  • This gives us: \[ x = 423 \]


Now, we see that 35.25% of 1200 equals 423.
Solving multiplication problems like this helps in various scenarios, such as calculating discounts, interest rates, or any percentage-based calculations.

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

Elijah collects baseball memorabilia. He bought two autographed plaques, but then became short of funds and had to sell them quickly for \(\$ 200\) each. On one, he made a \(20 \%\) profit, and on the other, he lost \(20 \% .\) Did he make or lose money on the sale?

Solve. The sales tax rate in Miami, Florida, is \(1 \%\) for Dade County plus \(6 \%\) for the state. Find the total amount paid for 2 tires at \(\$ 49.95\) each.

Solve. The sales tax is \(\$ 35.80\) on the purchase of a refrigeratorfreezer that sells for \(\$ 895 .\) What is the sales tax rate?

The population of West Virginia in 2010 was \(1,852,994 .\) It is projected that the population of West Virginia will be 1,821,013 in 2020 . What will the percent decrease be?

Solve. Animal Instinct Pet Supply borrows \(\$ 6500\) at \(5 \frac{1}{4} \%\) for 90 days. Find (a) the amount of interest due and (b) the total amount that must be paid after 90 days.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.