/*! 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 40 Solve each equation. $$ \fra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 40

Solve each equation. $$ \frac{20}{100}=\frac{z}{80} $$

Short Answer

Expert verified
z = 16

Step by step solution

01

Set up the equation

We start with the given equation: \( \frac{20}{100} = \frac{z}{80} \)
02

Cross-multiply

To eliminate the fractions, cross-multiply the terms. This gives us: \( 20 \cdot 80 = 100 \cdot z \)
03

Perform the multiplication

Calculate the multiplication on the left side: \( 1600 = 100z \)
04

Solve for \(z\)

Divide both sides by 100 to isolate \(z\): \( z = \frac{1600}{100} \)
05

Simplify the result

Simplify the fraction: \( z = 16 \)

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.

Cross-Multiplication
Cross-multiplication is a technique used to solve equations that involve fractions. When we have a proportion, like \(\frac{a}{b} = \frac{c}{d}\), cross-multiplication allows us to eliminate the fractions by multiplying across the equal sign. This involves multiplying the numerator of one fraction by the denominator of the other fraction.

For example, in the equation \(\frac{20}{100} = \frac{z}{80}\), we can cross-multiply to get:
  • \(20 \times 80\) on one side
  • \(100 \times z\) on the other side
This simplifies to \(1600 = 100z\), allowing us to move to the next step.
Isolating Variables
The next step in solving an equation is to isolate the variable (in this case, \(z\)). Isolating a variable means getting the variable by itself on one side of the equation. This often involves dividing or multiplying both sides of the equation by the same number.

In our example, after cross-multiplying, we have the equation \(1600 = 100z\). To isolate \(z\), we need to get rid of the 100, which is currently being multiplied by \(z\). We do this by dividing both sides of the equation by 100:
  • \(\frac{1600}{100} = \frac{100z}{100}\)
The result is \(z = 16\). Now we have isolated \(z\) and found its value.
Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form. This means making the numerator and the denominator as small as possible while still keeping the same ratio.

In our example, when we isolated \(z\), we ended with \(\frac{1600}{100}\). To simplify this, we divide both the numerator and the denominator by their greatest common divisor (GCD).

For \(1600\) and \(100\), the GCD is \(100\). So, we perform the division:
  • \(\frac{1600}{100} = 16\)
Therefore, \(z\) simplifies to \(16\). By breaking down the steps, we ensure the fraction is in its simplest form, making the solution clear and easy to understand.

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

Find the measure of an angle whose complement is four times its measure. (Hint: If \(x\) represents the measure of the unknown angle, how would we represent its complement?)

To see the connection between the solution of an equation and the solutions of the corresponding inequalities. Solve the following inequality, and graph the solution set on a number line. \( 3 x+2>14 \)

If 2 is added to five times a number, the result is equal to 5 more than four times the number. Find the number.

If 4 is added to twice a number and this sum is multiplied by \(2,\) the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?

Solve each equation for \(y\) $$ 3 x+y=6 $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.