/*! 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 11 Ron bought \(x\) dollars worth o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 11

Ron bought \(x\) dollars worth of stock and paid a \(y\) percent commission. Dave purchased \(p\) dollars worth of stock and paid a \(q\) percent commission, where \(x>p .\) Pick numbers for \(x, y, p,\) and \(q\) such that Ron's commission is less than Dave's.

Short Answer

Expert verified
If Ron invests \$100 at a 2% commission (yielding a \$2 commission), and Dave invests \$50 at a 10% commission (resulting in a \$5 commission), even though Ron invests more, his commission is less than Dave's commission. Satisfactorily satisfying the exercise conditions.

Step by step solution

01

Define Variables

Let's start by defining the variables in such a way that Ron's commission is less than Dave's. Let's suppose \(x = 100\), \(y = 2\), \(p = 50\), and \(q = 10\). Here, \(x > p\) (as defined in the problem), and we need to ensure that \(2\%\) of \$100 is less than \(10\%\) of \$50.
02

Calculate Ron's commission

Calculate Ron's commission by multiplying \(x\) and \(y\) and then dividing by 100, as \(y\) is a percentage. This gives us \(100 * 2 / 100 = 2\). This means Ron's commission is \$2.
03

Calculate Dave's commission

Next, we calculate Dave's commission by multiplying \(p\) and \(q\) and then dividing by 100, because \(q\) is a percentage. This gives us \(50 * 10 / 100 = 5\). This means, Dave's commission is \$5.
04

Compare Commissions

Finally, we see that Ron's commission (\$2) is indeed less than Dave's commission (\$5). Therefore, the selected numbers meet the requirements of the exercise.

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.

Stock Investments
Stock investments involve buying shares in a company. By purchasing these shares, you are essentially buying a portion of the company. The value of stocks fluctuates based on the company鈥檚 performance and market conditions. When investing in stocks, it鈥檚 important to consider:
  • Risk Tolerance: Stocks can be volatile. Understanding how much risk you are willing to bear is essential.
  • Diversification: Spread your investments across different sectors to minimize risk.
  • Investment Goals: Consider whether you are investing for short-term gains or long-term growth.
When Ron and Dave invested in their stocks, they each chose different amounts to invest. Ron chose a higher amount than Dave, but the commission they paid depended not just on the amount invested but also on the commission percentage rate.
Commission Calculation
The commission is the fee paid to process a stock transaction. It is typically calculated as a percentage of the total transaction amount. Here鈥檚 how you calculate the commission:- **Formula**: Commission = (Investment Amount * Commission Rate) / 100For example, Ron鈥檚 investment of \(100 at a 2% commission resulted in a commission of \(\frac{100 \times 2}{100} = 2 \) dollars. Similarly, Dave鈥檚 investment of \)50 at a 10% commission resulted in a commission of \(\frac{50 \times 10}{100} = 5\) dollars. This shows how even smaller investments can lead to higher commissions if the commission rate is higher. Understanding how to calculate commissions is useful not only for comparing costs but also for making informed investment decisions.
Inequalities in Mathematics
In this problem context, inequalities are used to compare the commissions Ron and Dave paid. Understanding inequalities helps you analyze and solve problems where conditions must meet specific criteria. Here, the inequality provided was: - **Condition**: Ron's commission < Dave's commission By substituting the commissions we calculated: - **Comparison**: 2 < 5 This inequality holds true, fulfilling the problem's requirement. Inequalities are crucial when making comparisons in real-world scenarios, such as determining the most cost-effective investment or understanding the impact of rates and percentages. They allow you to make informed decisions by clearly showing one value is greater or smaller than another.

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

In Exercises 6鈥�9, use the method illustrated in Example 2 to determine moving averages by subtraction and addition. Determine the 2 -day SMA for the ten consecutive day closing prices for Toyota Motor Corp listed below. \(\$ 101.96, \$ 101.80, \$ 101.50, \$ 103.07, \$ 104.94\) \(\$ 105.12, \$ 105.66, \$ 104.76, \$ 100.56, \$ 101.31\)

You own \(K\) shares of a stock that is selling for \(x\) dollars per share. The quarterly dividend is \(y\) dollars per share. a. Express the annual dividend for one share algebraically. b. Express the annual dividend for all \(k\) shares algebraically. c. Express the yield as an algebraic fraction.

Mitchell bought 600 shares of Centerco two years ago for \(\$ 34.50\) per share. He sold them yesterday for \(\$ 38.64\) per share. a. What was the percent increase in the price per share? b. What was the total purchase price for the 600 shares? c. What was the total selling price for the 600 shares? d. What was the percent capital gain for the 600 shares? e. How does the percent increase in the price of one share compare to the percent capital gain for all 600 shares?

Laura bought 55 shares of stock for \(\$ 3.50\) per share last year. She paid her broker a 1\(\%\) commission. She sold the stock this week for \(\$ 2\) per share, and paid her broker a \(\$ 10\) flat fee. a. What were Laura's net proceeds? Round to the nearest cent. b. What was her capital gain or loss?

A corporation is having a shareholders meeting. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by \(2,351,000\) shares of stock owned by \(111,273\) shareholders. a. Must all of the shareholders own more than one share of stock? b. If \(3,411\) shareholders attend the meeting, what percent of the shareholders are represented? Round to the nearest percent. c. If the shareholders who do attend own a combined 1.8 million shares of the corporation, what percent of the shares are represented at the meeting? Round to the nearest percent.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.