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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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## Unit 10: Lesson 1

- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example

## Systems of linear equations word problems — Basic example

## Want to join the conversation?

## Video transcript

## SUBSTITUTION METHOD WORD PROBLEMS AND ANSWERS

Let "x" be the cost of each bat.

Let "y" be the cost of each ball.

Substitute y = (3800 - 7 x)/6 in (2)

(2)-----> 3x + 5(3800 - 7x)/6 = 1750

(3)-----> y = [3800 - 7(500)] / 6

So, the cost of each bat is $500 and each ball is $50.

Let "y" be the charge per km for the distance covered

Substitute x = 105 - 10y in (2).

(2)-----> 105 - 10y + 15y = 155

Therefore, the fixed charge is $5 and charge per km for the distance covered is $10.

Amount has to be paid for a travel of 25 km is

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## Writing Systems of Linear Equations from Word Problems

(i) There are two different quantities involved: for instance, the number of adults and the number of children, the number of large boxes and the number of small boxes, etc. (ii) There is a value associated with each quantity: for instance, the price of an adult ticket or a children's ticket, or the number of items in a large box as opposed to a small box.

Here are some steps to follow:

Understand all the words used in stating the problem. Understand what you are asked to find. Familiarize the problem situation.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Use substitution , elimination or graphing method to solve the problem.

The admission cost for 12 children and 3 adults was $ 162 . The admission cost for 8 children and 3 adults was $ 122 .

2 . Translate the problem to an equation.

Let x represent the admission cost for each child. Let y represent the admission cost for each adult. The admission cost for 12 children plus 3 adults is equal to $ 162 . That is, 12 x + 3 y = 162 . The admission cost for 8 children plus 3 adults is equal to $122. That is, 8 x + 3 y = 122 .

3 . Carry out the plan and solve the problem.

Subtract the second equation from the first. 12 x + 3 y = 162 8 x + 3 y = 122 _ 4 x = 40 x = 10 Substitute 10 for x in 8 x + 3 y = 122 . 8 ( 10 ) + 3 y = 122 80 + 3 y = 122 3 y = 42 y = 14 Therefore, the cost of admission for each child is $ 10 and each adult is $ 14 .

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## IMAGES

## VIDEO

## COMMENTS

The four steps for solving an equation include the combination of like terms, the isolation of terms containing variables, the isolation of the variable and the substitution of the answer into the original equation to check the answer.

The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

Linear equations were invented in 1843 by Irish mathematician Sir William Rowan Hamilton. He was born in 1805 and died in 1865. Through his algebraic theory, Sir Hamilton made important contributions to mathematics, and his work found appli...

key idea. To solve using substitution, follow these four steps: Step 1: Isolate a variable. Step 2: Plug the result of Step 1 into the other equation and solve

Write a system of linear equations to represent each scenario. The solve the system using substitution. 5. Randy wants to join a gym to lose his winter weight.

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http://www.freemathvideos.com In this video series I will show you how to solve a word problem by setting up a system of equations.

Steps For Solving Real World Problems · Highlight the important information in the problem that will help write two equations. · Define your variables · Write two

Step 1: Define your variables. Step 2: Write equations with the variables that represent the scenario in the word problem. Step 3: Pick one of the equations and

If you use substitution method, you solve one of the equations for a single variable. For example, change K+L=450 into K=450-L. You can then use the value of "k

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Now one issue to think about, and there's many ways to solve these, is if we just add the left hand sides of this equation and add the right

Problem 1 : The coach of a cricket team buys 7 bats and 6 balls for $3800. · Solution : Let "x" be the cost of each bat. · Problem 2 : The taxi charges in a city

Writing Systems of Linear Equations from Word Problems ; 1 . Understand the problem: ; 2 . Translate the problem to an equation. ; 3 . Carry out the plan and solve