/*! 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 20 Solve proportion. \(\frac{6}{z... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 20

Solve proportion. \(\frac{6}{z-3}=\frac{15}{z}\)

Short Answer

Expert verified
z = 5

Step by step solution

01

Cross Multiply

To solve the proportion \( \frac{6}{z-3}=\frac{15}{z} \), start by cross multiplying to eliminate the fractions. This gives \[ 6 \times z = 15 \times (z - 3) \].
02

Distribute and Simplify

Distribute the 15 on the right-hand side: \[ 6z = 15z - 45 \].
03

Isolate the Variable

Subtract 15z from both sides to isolate the variable on one side: \[ 6z - 15z = -45 \], which simplifies to \[ -9z = -45 \].
04

Solve for z

Divide both sides by -9 to solve for \( z \): \[ z = \frac{-45}{-9} = 5 \].

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 method to solve proportions, which are equations that state two ratios are equal. When given a proportion like \(\frac{6}{z-3}=\frac{15}{z}\), cross multiplication helps to eliminate the fractions by multiplying the numerator of one side by the denominator of the other side. In this case, you multiply 6 by \(z\) and 15 by \(z-3\), which results in the equation: \[6 \times z = 15 \times (z - 3)\].
This step makes it easier to work with the equation, as it turns a proportion into a linear equation, which can then be simplified and solved.
solving linear equations
Solving linear equations involves finding the value of the variable that makes the equation true. After cross multiplying the original proportion, you get the equation: \[6z = 15(z-3)\].
The next step is to simplify this equation. You'll need to distribute the 15 to both terms inside the parentheses. This means you multiply 15 by both \(z\) and -3, resulting in: \[6z = 15z - 45\].
By simplifying the equation, you're one step closer to isolating the variable and finding its value.
isolating variables
Isolating the variable involves getting the variable alone on one side of the equation. From the previous simplified equation \[6z = 15z - 45\], you need to get all the terms containing \(z\) on one side and the constant terms on the other. You do this by subtracting 15z from both sides:
\[6z - 15z = -45\].
This simplifies to \(-9z = -45\).
Now the variable \(z\) is isolated on one side of the equation, making it easier to solve for its value.
simplifying equations
Simplifying equations means performing operations to make the equation easier to solve. Now that you have the equation \(-9z = -45\), the next step is to solve for \(z\).
Divide both sides by -9 to get:
\[z = \frac{-45}{-9} = 5\].
Here, the equation is simplified to \(z = 5\).
Remember, keeping equations simple at each step makes solving them more manageable and reduces the chances of making mistakes.

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 geometric mean between 36 and 4

In Exercises \(1-8,\) use the Pythagorean Theorem to find the length of the missing side in right triangle \(\triangle A B C\) with right angle \(C\). If \(a=12\) yd and \(b=5\) yd, find \(c\)

Solve each inequality and give a reason for each step in the solution. $$\frac{y+3}{-2} < 17$$

Write ratio as a fraction and simplify. \(\frac{1}{2}\) in. to \(\frac{3}{8}\) in

Prove that the ratio of the lengths of the altitudes from corresponding angles in similar triangles equals the ratio of the lengths of any two corresponding sides.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied 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.