Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. She has 20 years of experience teaching collegiate mathematics at various institutions.
Practicing Mixture Problems in Algebra
Definition & Steps
Mixture problems in algebra involve combining things such as solutions or objects together to create a desired blend. Although there are multiple types of mixture problems in algebra, they all follow the same basic solving process. In this lesson, we will practice by solving problems that involve adding or taking away an element from a solution to obtain a new solution as well as mixing two solutions together to obtain a new solution.
![]() |
Solving these types of problems takes on the general pattern of the following four steps.
1.) Use a variable to represent the unknown quantity in the problem.
2.) Use the information given in the problem to create an equation involving that variable.
3.) Use algebra to solve the equation for the variable.
4.) Answer the question posed in the problem.
We want to look at multiple examples to practice solving mixture problems. In each of the following practice problems, we will use the four steps listed above as a guide to help us solve the problem.
Practice Problem #1
Suppose you have a jug of 120 ounces of juice that is 20% pure apple juice and the rest is water. You feel this is a bit too sweet, so you want to add water to the juice so that your new juice is 15% pure apple juice. How much water should you add?
Solution:
1.) Your unknown quantity is how much water you should add to your juice. We will represent this with the variable w.
2.) We want to set up an equation in w with the information given.
The initial jug of juice is 120 ounces, and it contains 20% pure apple juice. We can figure out how many ounces of pure apple juice are in the jug by finding 20% of 120 ounces. We convert 20% to decimal form by multiplying by 1 / 100 to get 0.20. Then we multiply 120 by 0.20. Thus, we have 120 * 0.20 = 24 ounces.
We are adding w ounces of water to our initial juice, so our new juice will contain 120 + w ounces, and 24 of those ounces will still be pure apple juice. We want this new juice to be 15% pure apple juice, so we want 24 to be 15% of 120 + w. Putting this into an equation, we have 0.15( 120 + w ) = 24. This is our equation.
3.) Now we will solve our equation using algebra.
![]() |
4.) We see that w = 40 ounces, so we should add 40 ounces of water to our jug of juice in order to have a juice that is 15% pure apple juice.
Practice Problem #2
Assume you have 15 gallons of a 15% oil solution. How many gallons of a 30% oil solution need to be added to make a 25% oil solution?
Solution:
1.) You're unknown quantity is how many gallons of the 30% oil solution you should add to your 15% oil solution. We will represent this with the variable s.
2.) We want to set up an equation in s with the information given.
Our initial solution is 15 gallons of 15% oil solution. To find the number of gallons of oil our initial solution contains, we convert 15% to decimal form (as previously demonstrated) to get 0.15. Then we multiply by the 15 gallons. Our initial solution contains 15 * 0.15 = 2.25 gallons of oil. The solution we are adding is s gallons of 30% oil solution, so this solution contains 0.30s gallons of oil.
When we mix these two solutions together, we have s + 15 gallons of mixture, and we want 25% of that to be oil, so we want our mixture to contain 0.25( s + 15) gallons of oil.
Putting this all together to create an equation, we recognize that the amount of oil in the 15% solution (2.25 gallons) plus the amount of oil in the added 30% solution (0.30s gallons) will be equal to the amount of oil in the desired final mixture (0.25(s +15) gallons). In equation form, we have 2.25 + 0.30s = 0.25( s + 15).
3.) Now we solve the equation we found in step 2 using algebra.
![]() |
4.) We see that s = 30 gallons, so we should add 30 gallons of our 30% oil solution to our 15 gallons of our 15% oil solution to obtain a 25% oil solution.
Practice Problem #3
Assume you have 500 milliliters of saline solution (salt and water) that is 4% salt. How much water must evaporate to get a saline solution that is 8% salt?
Solution:
1.) Our unknown quantity is how much water must evaporate to get a saline solution with 8% salt. We will represent this with the variable x.
2.) Our original solution is 500 milliliters of saline solution that is 4% salt. Thus, we convert 4% to decimal form and multiply by 500 to find that it contains 500 * 0.04 = 20 milliliters of salt. When x milliliters of water are evaporated, we will have 500 - x milliliters of saline solution, which will still contain 20 milliliters of salt. We want those 20 milliliters to be 8% of our 500 - x milliliters of saline solution. In equation form, we have 0.08( 500 - x ) = 20.
3.) Now we use algebra to solve our equation.
![]() |
4.) We see that x = 250 milliliters, so 250 milliliters of water must evaporate from our original saline solution to obtain a saline solution that is 8% salt.
Lesson Summary
To solve mixture problems in algebra, we follow these four steps.
1.) Represent the unknown quantity with a variable.
2.) Create an equation involving that variable.
3.) Solve the equation for the variable.
4.) Answer the question posed in the problem.
The practice problems in this lesson have given us the chance to become more comfortable with these steps. The more you practice these types of problems, the easier they will become, and you will familiarize yourself with the pattern of the solving process. Just remember, practice makes perfect!
To unlock this lesson you must be a Study.com Member.
Create your account
Register to view this lesson
Unlock Your Education
See for yourself why 30 million people use Study.com
Become a Study.com member and start learning now.
Become a MemberAlready a member? Log In
BackPracticing Mixture Problems in Algebra
Related Study Materials
- TExES Science of Teaching Reading (293): Practice & Study Guide
- Next Gen NCLEX-PN Study Guide & Practice
- Next Gen NCLEX-RN Study Guide & Practice
- TExES Core Subjects EC-6 (391): Practice & Study Guide
- TExES School Counselor (252): Practice & Study Guide
- Teaching Vocabulary Acquisition
- The Changing Earth
- Power, Work and Energy
- States of Matter and Chemistry
- Legal and Ethical Issues in School Psychology
- How to Pick Your Homeschool Curriculum
- Role of Student Support in Open & Distance Learning
- TExES Principal Exam Redesign (068 vs. 268)
- Teacher Salary by State
- ESL Resource Guide for Teachers
- What is a Homeschool Co-op?
- How to Start Homeschooling Your Children
Latest Courses
- Mechanistic & Organic Organizational Business Structures
- Chemical Nomenclature & Notation
- Factors Impacting Family & Consumer Sciences
- Heritability Coefficient
- What is Batik? - Art & Fabrics
- Suspicious Activity Reports & Federal Statutes
- Sadako and the Thousand Paper Cranes: Author & Genre
- What are Dinosaurs Related to? - Quiz & Worksheet for Kids
- Quiz & Worksheet - Common Health Problems in the US
- Quiz & Worksheet - Memory Hole in 1984
- Quiz & Worksheet - Types of Personality Disorders
- Flashcards - Real Estate Marketing Basics
- Flashcards - Promotional Marketing in Real Estate
- Music Lesson Plans
- Middle School Math Worksheets
Latest Lessons
- World Conflicts Since 1900
- SAT Prep: Practice & Study Guide
- PSAT Prep: Tutoring Solution
- NY Regents Exam - US History and Government: Tutoring Solution
- Intro to Physics for Teachers: Professional Development
- Moral Issues in Economic Equality & Poverty
- Ethics in the Workplace: Help and Review
- Quiz & Worksheet - Evolutionary Relationships
- Quiz & Worksheet - Moksha
- Quiz & Worksheet - Arpeggio
- Quiz & Worksheet - Blastula Stage
- Quiz & Worksheet - Kingdom Protista
Popular Courses
- The Cotton Club: History, Performers & Harlem Renaissance
- Ancient Egyptian God Khepri: Mythology, Symbol & Facts
- Book Club Suggestions
- Love Quotes in Translated Literature
- Math Project Rubrics
- Special Education Private Schools in California
- What Are The TELPAS Language Proficiency Levels?
- Jobs for Teachers Outside of Education
- Persuasive Writing Topics for Kids
- Ethos, Pathos & Logos Lesson Plan
- 5th Grade Common Core Math Standards
- NYS Geometry Regents Exam Information
Popular Lessons
Math
Social Sciences
Science
Business
Humanities
Education
History
Art and Design
Tech and Engineering
- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers
Health and Medicine
- A chemist needs 170 milliliters of a 52% solution but has only 32% and 66% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
- Dan needs 12 gallons of 15% bleach. He has 10% bleach and 30% bleach. If he mixes these two bleach solutions together to get his 12 gallons of 15% bleach, how many gallons of the 10% bleach will he ne
- A 5-liter cleaning solution contains 30% bleach. A 3-liter cleaning solution contains 50% bleach. What percent of bleach is obtained by combining the two mixtures together?
- A container is filled with 100 grams of bird feed that is 80% seed. Tom and Sally want to mix the 100 grams with bird feed that is 5% seed to get a mixture that is 40% seed. Tom wants to add 114 grams