/*! 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 37 Solve. $$ \frac{x}{188}=\fra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 37

Solve. $$ \frac{x}{188}=\frac{2}{47} $$

Short Answer

Expert verified
x = 8

Step by step solution

01

Cross-Multiply

To solve the equation \( \frac{x}{188} = \frac{2}{47} \), start by cross-multiplying. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction. This gives us the equation: \[ x \times 47 = 2 \times 188 \]
02

Simplify the Equation

Next, simplify both sides of the equation from Step 1. Calculate the products: \[ 47x = 376 \]
03

Isolate the Variable

Divide both sides of the equation by 47 to solve for \( x \). \[ x = \frac{376}{47} \] Simplify this to find: \[ x = 8 \]

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.

Solving Equations
To solve equations, especially those containing fractions, we often use a method called cross-multiplication. This method involves multiplying across the equality of two fractions. It's a technique that can simplify solving for an unknown variable, making it easier to isolate and find its value.
Sometimes, equations appear complicated, but breaking them into smaller steps, you can solve them more easily.
Don't rush through the steps. Let's look at how to solve using a specific example.
Fractions
Fractions are simply numbers that express a part of a whole. In the equation, \(\frac{x}{188} = \frac{2}{47}\), we are dealing with fractions. To solve such equations, we apply concepts like cross-multiplication.
Understanding the components of a fraction鈥攏umerator (top part) and denominator (bottom part)鈥攊s key.
When you cross-multiply, you are essentially balancing both fractions by equalizing their parts.
Isolate the Variable
After cross-multiplying, the next step is to isolate the variable. Here's what we do step-by-step:
  • First, simplify the products after cross-multiplying.
  • Next, divide both sides by the number that is multiplied by the variable, in this case, 47.
For our example, starting from the equation 47x = 376, we'll divide both sides by 47:
\[ x = \frac{376}{47} \]\ years.
The right-hand side simplifies further to find x = 8. By isolating the variable, we now know that the unknown value x equals 8.
Simplification
Simplification is a critical part of solving equations. It involves reducing the equation to its simplest form.
For the example equation, after cross-multiplying, we simplified the products 47x = 376.
Dividing both sides by 47 led us to \[ x = \frac{376}{47} \], which further simplifies to 8.
By performing these operations sequentially, we strip down the equation to its core, making it easier to handle.
Simplification helps us see and understand the relationship between the numbers and the unknown variable clearly.

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

The amount in a savings account increased from $$\$ 200$$ to $$\$ 216 .$$ What was the percent increase?

Solve. A family invests \(\$ 4000\) in an account paying \(6 \%\), compounded monthly. How much is in the account after 5 months?

Solve. Joshua earns \(\$ 120\) for selling \(\$ 2400\) worth of television sets. What is the commission rate?

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.

Find the prime factorization of 228 .
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.