Back To Course

GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

Instructor:
*Betsy Chesnutt*

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Understanding the relationship between cost, rate, and number of units will allow you to know how much a group of items will cost, determine the cost of a single item, and find the number of things you can buy with a certain amount of money.

Imagine that you want to purchase 5 books that cost $3 each. What will be the total cost? Before we can figure out how much money you need to buy your new books, there are three important terms that we need to define: cost, rate, and number.

**Cost** (*c*) is the total cost of the purchase.

**Rate** (*r*) is the cost of EACH individual item.

**Number** (*n*) is the number of items you want to purchase.

These are related in the following way:

*c* = *n**r*

This means that to find the total cost of a group of items, you need to multiply the rate (*r*) by the number (*n*).

For example, if you want to buy those 5 books that cost $3 each, the total cost will be $15.

*n* = 5 and *r* = $3, so *c* = (5) ($3) = $15

In addition to finding the total cost of a group of items, you may also need to find the number of items when you know the cost and rate. For example, suppose you go to the store to buy some apples and see that apples are $0.88 each. You have $10 and want to know how many apples you can buy.

In this situation, you know the cost ($10) and the rate ($0.88), but you don't know the number you can buy. Even though this seems different from the first problem at first, you can still use the same relationship. It just needs to be rearranged first.

Start with *c* = *n**r*. Then to find *n*, you need to divide both sides of the equation by *r*. This gives you *n* = *c* / *r*. Now, you are ready to find the number of apples you can buy.

*n* = *c* / *r* = $10 / $0.88 = 11.4 apples

Since the store probably won't let you cut up an apple before you buy it, this means you can only buy 11 apples with your $10.

Another common problem involves finding the rate when you know the number and cost. For example, if you started a new job and were told you would be paid $100 for each eight-hour day you worked, how much money would you be making per hour?

Once again, start with *c* = *n**r*. This time, to find *r*, you need to divide both sides of the equation by *n*. This gives you *r* = *c* / *n*. In this situation, 8 would be the number, and $100 would be the cost (even though you aren't buying anything, it is still the total amount).

*r* = *c* / *n* = $100/8 = $12.50

So, you will be making $12.50 each hour that you work at your new job.

Now that you have seen how to find the cost, rate, or number, let's look at a few practice problems to make sure that you really understand all the different ways to use this formula.

Oranges cost $1.50 a pound. If you buy 5 lbs of oranges, how much will it cost?

Solution:

To answer this, first think about what quantities you already know and what you need to find. You know the rate ($1.50 per pound) and the number (5 lbs), and you need to find the cost (*c*), so we can use *c* = *n**r*.

*c* = ($1.50) (5) = $7.50

So, 5 lbs of oranges will cost $7.50.

You buy 12 batteries for a total cost of $6.00. How much did each battery cost?

Solution:

In this problem, you know the cost ($6.00) and number (12), but not the rate, so you want to use *r* = *c* / *n* .

*r* = $6.00 / 12 = $0.50

This means that each battery cost you $0.50.

You have $40 and want to buy some flowers that cost $2.50 each. How many can you buy?

Solution:

Now, you know the cost ($40) and the rate ($2.50), but not the number, so you want to use *n* = *c* / *r*.

*n* = $40 / $2.50 = 16

With $40, you will be able to buy a total of 16 flowers if they each cost $2.50.

To find the total **cost** of a group of items, you need to known both the **rate** charged for each item and the **number** of items you want to buy.

*c* = *n**r*

You can also rearrange this equation to find the number or rate if you already know the total cost.

*n* = *c* / *r*

*r* = *c* / *n*

Understanding the relationship between cost, rate, and number will allow you to know how much a group of items will cost, to determine the cost of a single item if you know the total, or to find the number of things you can buy with a certain amount of money.

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
5 in chapter 3 of the course:

Back To Course

GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

- DSST Information Guide
- GACE Early Childhood Special Education General Curriculum: Practice & Study Guide
- TExMAT Master Mathematics Teacher EC-4 (087): Study Guide & Practice
- ILTS Gifted Education: Practice & Study Guide
- Academic Writing Essentials
- Programming Basics in C++
- C++ Programming Functions
- Required Assignments for Criminal Justice 381
- Studying for Art 103
- Student Grouping Strategies
- CTEL Test Score Information
- CTEL Test Accommodations
- CTEL Test Retake Policy
- CSET Test Day Preparation
- How to Study for the VCLA Test
- Can You Use a Calculator on the CBEST?
- CTEL Registration Information

- Common Adverbial Clauses & the Subjunctive in Spanish
- Prison Reform: History, Issues & Movement
- Writing a Play: Script Format, Steps & Tips
- How Are ELL Students Identified?
- Helping Employees Identify Personal & Organizational Challenges
- Using Protagonists in Visual Media to Tell a Story
- Encapsulation C++ Programming: Definition & Example
- Program Memory in C++ Programming
- Quiz & Worksheet - Assessing the Cultural Background of ELL Students
- Quiz & Worksheet - Manorialism
- Quiz & Worksheet - Chromic Acid Test Reaction
- Quiz & Worksheet - West Egg in The Great Gatsby
- Quiz & Worksheet - Identifying & Analyzing Text Structure
- Flashcards - Introduction to Research Methods in Psychology
- Flashcards - Clinical Assessment in Psychology

- MTTC Sociology (012): Practice & Study Guide
- Excel: Skills Development & Training
- Creating a Framework for Competitive Analysis
- FTCE Business Education 6-12 (051): Test Practice & Study Guide
- Understanding Customer Relationship Management Basics
- ScienceFusion Space Science Unit 2.6: Small Bodies in the Solar System
- CUNY Assessment Test in Math: Ratios & Proportions
- Quiz & Worksheet - Irony in Julius Caesar
- Quiz & Worksheet - Multiplication & Exponents
- Quiz & Worksheet - General Partnership in Business Law
- Quiz & Worksheet - Measurement of Adult Development & Aging Research
- Quiz & Worksheet - Reversible or Apparent Dementias

- How to Compare Integers
- Jelly Roll Morton: Biography, Songs & Music
- In-School Resources for Teacher Professional Development
- Response to Intervention (RTI) in Georgia
- Resources for District, State & National Education Standards
- How Does Tuition Reimbursement Benefit the Employer?
- MCAT Score Percentiles
- Homeschool vs. Public School Statistics
- Minnesota State Language Arts Standards
- Is the TABE Test Hard?
- Paragraph Writing Rubrics
- Homeschooling in South Dakota

Browse by subject