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## Real World: Solving Systems of Equations Word Problems

Also included in: Solving Systems of Equations Activity Bundle

## Solving Systems of Equations from Word Problems Activity | Mystery Algebra 1

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## Solving Systems of Equations Word Problems - Notes & Homework

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## Writing and Solving Systems of Equations Word Problems Jumbo Task Cards

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## Systems of Equations Word Problems | Solving Systems of Linear Equations

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## Solve Systems of Equations Given Word Problems Exam (Mrs Math)

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## Solving Systems of Equations Word Problems (by Substitution)

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## Gotta Solve 'em All: Metric System Word Problem Task Cards 4.MD.2

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## R.U.L.E.S. for Solving Systems of Equations Word Problems Powerpoint

## Apply Systems of Equations Word Problems Solve & Flip

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## Solving Systems Word Problems Practice

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## HSA-BF.A.1 Algebra 1 Unit 2 Complete Lesson 13 Solve System of Eq Word Problems

## Setting Up Solving Systems of Equations Word Problems

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## Solving Systems of Linear Equations Word Problems Practice - Task Card Game

Also included in: Systems of Equations Word Problems - Notes, Practice & Activity SKILL BUNDLE

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## Solving Systems of Equations Word Problems Worksheets

## Aligned Standard: HSA-REI.C.5

- Carpenter's Project Step-by-step Lesson - We're making chairs, but at what rate and how often?
- Guided Lesson - Making muffins, pearl necklaces, and making sandwiches.
- Guided Lesson Explanation - Create the system first and then find the sweet spot that they both fit into.
- Practice Worksheet - Our scenarios include candle making, buying books and fruit juices.
- Matching Worksheet - Fill in the missing numbers to make each word problem mathematically correct.
- Answer Keys - These are for all the unlocked materials above.

## Homework Sheets

Some of these problems were so hard to get right that it took several tries.

- Homework 1 - A test has 20 questions worth a total of 100 points. There are two question types on the test. Matching questions are worth 4 points and multiple choice questions are worth 6 points. How many multiple choice and matching questions are there each?
- Homework 2 - 3 small vases and one large vase hold 6 liters of water. If you poured a full large vase into a small vase and filled it, you would still have 2 liters of water left in the large vase. How much water can a large vase hold?
- Homework 3 - Billy went to the fun park. He rode the water slide 5 times and the Ferris wheel twice. He spent $20 on the rides. Jenny rode the water slide 3 times and the Ferris wheel 3 times. Jenny spent $21 on rides. How much does it cost to go on the water slide?

## Practice Worksheets

The flow here is set up to make students work a little harder as they go along.

- Practice 1 - Shelly wants to make cookies. She has two different sized cooking pans. She only uses one pan per flavor of cookie. On Saturday, she makes 12 pans of chocolate cookies and 10 pans of vanilla cookies for a total of 312 cookies. On Sunday, She makes 5 pans of chocolate cookies and 3 pans of vanilla cookies for a total of 116 cookies.
- Practice 2 - Ash sells dumplings at the local farmer’s market. On Monday, he sold 12 veggie dumplings and 15 meat dumplings for $69. On Tuesday, he sold 18 veggie dumplings and 7 meat dumplings for $57.
- Practice 3 - The sum of two numbers is 26. The difference of the same two numbers is 8. What are the numbers?

## Math Skill Quizzes

The quizzes were hard to get set correctly. It took me a while to get the numbers to balance.

- Quiz 1 - Kelly had a great basketball game today. She made 39 points with 16 different shots. If she only made two and three point shots, how many of each did she make?
- Quiz 2 - At the movies, an adult ticket costs $9 and a kid’s ticket costs $6. If Mr. Fluffy brought 9 people and spent $69, how many kids did he pay for?
- Quiz 3 - A Snickers bar has 150 more calories than a large chocolate chip cookie. Donnie has 3 Snickers bars and 4 chocolate chip cookies for a total of 1,150 calories. How many calories are in each Snickers bar and Chocolate chip cookie?

## What Are Systems of Equations in Math?

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## Solving Systems of Equations Real World Problems

## Steps For Solving Real World Problems

- Highlight the important information in the problem that will help write two equations.
- Define your variables
- Write two equations
- Use one of the methods for solving systems of equations to solve.
- Check your answers by substituting your ordered pair into the original equations.
- Answer the questions in the real world problems. Always write your answer in complete sentences!

## Example 1: Systems Word Problems

1. Let's start by identifying the important information:

Let x = the number of hot dogs sold

Let y = the number of sodas sold

1.50x + 0.50y = 78.50 (Equation related to cost)

x + y = 87 (Equation related to the number sold)

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6. Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7. Check your work by substituting.

Since both equations check properly, we know that our answers are correct!

## Example 2: Another Word Problem

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25 (Equation representing your lunch)

4x + 2y = 10 (Equation representing your friend's lunch)

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

## Take a look at the questions that other students have submitted:

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Systems problem about hats and scarves

How much did Alice spend on shoes?

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

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## How to Solve Systems of Equations Word Problems? (+FREE Worksheet!)

Learn how to create and solve systems of equations word problems by the elimination method.

## Related Topics

- How to Solve One-Step Equations
- How to Solve One-Step Inequalities
- How to Solve Multi-Step Inequalities
- How to Solve Systems of Equations
- How to Graph Single–Variable Inequalities

## Step by step guide to solve systems of equations word Problems

- Find the key information in the word problem that can help you define the variables.
- Define two variables: \(x\) and \(y\)
- Write two equations.
- Use the elimination method for solving systems of equations.
- Check the solution by substituting the ordered pair into the original equations.

## Systems of Equations Word Problems – Example 1:

## Exercises for Solving Systems of Equations Word Problems

- A farmhouse shelters \(10\) animals, some are pigs and some are ducks. Altogether there are \(36\) legs. How many of each animal are there?
- A class of \(195\) students went on a field trip. They took vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds \(5\) students and each bus hold \(45\) students.
- The difference of two numbers is \(6\). Their sum is \(14\). Find the numbers.
- The sum of the digits of a certain two–digit number is \(7\). Reversing its increasing the number by \(9\). What is the number?
- The difference of two numbers is \(18\). Their sum is \(66\). Find the numbers.

## Download Systems of Equations Word Problems Worksheet

- There are \(8\) pigs and \(2\) ducks.
- There are \(3\) cars and \(4\) buses.
- \(10\) and \(4\).
- \(24\) and \(42\).

by: Reza about 3 years ago (category: Articles )

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