/*! 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 69 PREREQUISITE SKILL Solve each pr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 69

PREREQUISITE SKILL Solve each proportion. $$ \frac{6}{15}=\frac{8}{S} $$

Short Answer

Expert verified
The value of \( S \) is 20.

Step by step solution

01

Cross-Multiply

Cross-multiply the two fractions to create an equation. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction.The equation formed will be:\[ 6 imes S = 15 imes 8 \]
02

Solve the Equation

Simplify the equation obtained in Step 1 by performing the multiplication on the right side:\[ 6 imes S = 120 \]Next, solve for \( S \) by dividing both sides of the equation by 6:\[ S = \frac{120}{6} \]
03

Simplify the Solution

Perform the division on the right side to find the value of \( S \):\[ S = 20 \]

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 fundamental technique used to solve proportions, which are equations that show two ratios are equal. To use cross-multiplication, we follow these steps:
  • Take the numerator from the first fraction and multiply it by the denominator of the second fraction.
  • Do the same with the numerator of the second fraction and the denominator of the first fraction.
  • Set the two products equal to each other to form an equation.
For instance, given the proportion \( \frac{6}{15} = \frac{8}{S} \), we would multiply 6 by \( S \) and 15 by 8, forming the equation \( 6 \times S = 15 \times 8 \). This step is crucial because it helps us eliminate the fractions and work with a simpler equation to find the unknown value.
Solving Equations
Once you have formed an equation using cross-multiplication, the next step is to solve it. Solving equations involves finding the value of an unknown variable that makes the given statement true. Here's how it works in our example:
  • First, perform the multiplication indicated in the equation. For \( 6 \times S = 15 \times 8 \), simplify the right-hand side to get \( 120 \).
  • The equation then becomes \( 6 \times S = 120 \).
  • To isolate \( S \), divide both sides by 6, resulting in \( S = \frac{120}{6} \).
This process of simplifying and rearranging allows us to solve for \( S \), finding the value that will satisfy the original proportion.
Rational Expressions
Rational expressions are essentially fractions that involve variables. In the context of proportions, each side of the equation can be seen as a rational expression. Understanding how to manage these expressions is important for precise solutions. In our example:
  • The original proportions \( \frac{6}{15} \) and \( \frac{8}{S} \) are rational expressions because they include numbers and possibly variable denominators or numerators.
  • The goal is to manipulate these expressions to solve for the unknown variable, \( S \).
  • Cross-multiplication is particularly useful here as it simplifies the problem, converting rational expressions into a solvable linear equation without fractions.
By getting comfortable with rational expressions, you'll find it easier to handle other algebraic problems that involve fractions and unknown variables.

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

Determine the value of \(r\) so that a line through the points with the given coordinates has the given slope. (Lesson \(2-3 )\) $$ (r, 2),(4,-6) ; \text { slope }=-\frac{8}{3} $$

ACTINIIIES The band has 30 more members than the school chorale. If each group had 10 more members, the ratio of their membership would be \(3 : 2\) . How many members are in each group?

Find all of the zeros of each function. $$ g(x)=x^{4}-8 x^{2}-9 $$

Work A worker can power wash a wall of a certain size in 5 hours. Another worker can do the same job in 4 hours. If the workers work together, how long would it take to do the job? Determine whether your answer is reasonable.

CYCLING On a particular day, the wind added 3 kilometers per hour to Alfonso's rate when he was cycling with the wind and subtracted 3 kilometers per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 36 kilometers with the wind, he could go only 24 kilometers against the wind. What is his normal bicycling speed with no wind? Determine whether your answer is reasonable.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.