# Applications of Systems of Equations

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More Lessons for Basic Algebra
Math Worksheets

A series of free Basic Algebra Lessons.

In this lesson, we will learn

• mixture word problems
• rate word problems
• work word problems
• money word problems

### Mixture Problems

Some word problems using systems of equations involve mixing two quantities with different prices. To solve mixture problems, knowledge of solving systems of equations. is necessary. Most often, these problems will have two variables, but more advanced problems have systems of equations with three variables. Other types of word problems using systems of equations include rate word problems and work word problems.

Explains the concept of a value mixture problem and works this problem.
Example:
Two pounds of organic tea that costs \$6.75 a pound is mixed with some generic tea that costs \$3.25 a pound. How many pounds of the generic tea should be used to make a new tea mixture that costs \$4.65 a pound?

Mixture Problem
Example:
A special treat is made by mixing 5 pounds of popcorn costing \$.80 a pound with caramel costing \$2.40 a pound. How many pounds of caramel are needed to make a mixture that costs \$1.40 a pound?

Mixture Problem
Example:
Tina wants to mix some blackberries that cost \$2.75 a pound with 2 pounds of raspberries that cost \$3.50 a pound to get a mixture that costs \$3.25 a pound. How many blackberries should Tina buy?

### Rate Word Problems

To solve rate word problems, knowledge of solving systems of equations is necessary. Rate word problems include problems dealing with rates, distances, time and wind or water current. Other types of word problems using systems of equations include money word problems and age word problems.
Solves this word problem using uniform motion* rt = d* formula
Example:
Two cyclists start at the same corner and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hours, they are 81 miles apart. Find the rate of each cyclist.

Solves this word problem using uniform motion rt = d formula
Example:
A 555-mile, 5-hour trip on the Autobahn was driven at two speeds. The average speed of the car was 105 mph on the first part of the trip, and the average speed was 115 mph for the second part. How long did the car drive at each speed?

Algebra Word Problem: Distance, Rate, and Time.
This video shows an example about finding the speed of the current of stream.

### Work Word Problems

It is possible to solve word problems when two people are doing a work job together by solving systems of equations. To solve a work word problem, multiply the hourly rate of the two people working together times the time spent working to get the total amount of time spent on the job. Knowledge of solving systems of equations is necessary to solve these types of problems.
Linear Equation , Word Problem: Work, Rates, Time To Complete a Task.
Example:
Given that a person can complete a task alone in 32 hours and with another person they can finish the task in 19 hours. How long it would take the second person working alone?

Linear Equation , Word Problem : Work, Rates, Time To Complete a Task.
Example:
A drain is emptying a pool while a hose is filling the pool at the same time. Find how long it would take to fill the empty pool.

### Money Word Problems

Setting up a system of equations is usually effective when solving money word problems and word problems involving coins. A knowledge of how to solve systems of equations is necessary to solve these types of equations. Other types of word problems using systems of equations include mixture problems, rate word problems, work word problems and age word problems.
Algebra Money Word Problems with two variables (x and y). Solving equations with two variables

Algebra word problem involving money

Word problem involving coins and money

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 