How To Solve System Of Equations Word Problems

Solving Systems of Equations
Real World Problems

Wow! You have learned many dissimilar strategies for solving systems of equations! First we started with Graphing Systems of Equations. And so we moved onto solving systems using the Commutation Method. In our terminal lesson nosotros used the Linear Combinations or Addition Method to solve systems of equations.

At present we are ready to utilize these strategies to solve real world problems! Are you gear up? First allow's look at some guidelines for solving real earth issues and so we'll await at a few examples.

Steps For Solving Existent Earth Problems

Highlight the of import information in the trouble that will assist write two equations.

Ascertain 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.

Reply the questions in the real world problems. E'er write your answer in complete sentences!

Ok... let'south look at a few examples. Follow along with me. (Having a calculator will make information technology easier for you to follow along.)

Case 1: Systems Word Bug

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $i.50 and each soda costs $0.50. At the end of the night you fabricated a total of $78.50. You lot sold a full of 87 hot dogs and sodas combined. You must study the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

Solution

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

hot dogs cost $1.fifty
Sodas price $0.l
Made a total of $78.50
Sold 87 hot dogs and sodas combined

2. Define your variables.

Ask yourself, "What am I trying to solve for? What don't I know?

In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will represent. (Unremarkably the question at the end volition requite yous this information).

Let x = the number of hot dogs sold

Let y = the number of sodas sold

3. Write ii equations.

One equation will be related to the price and one equation will exist related to the quantity (or number) of hot dogs and sodas sold.

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

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

iv. Solve!

We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y.

Solving a systems using substitution

5. Think nearly what this solution means.

ten is the number of hot dogs and 10 = 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.

six. Write your respond in a consummate judgement.

35 hot dogs were sold and 52 sodas were sold.

seven. Check your work by substituting.

1.50x + 0.50y = 78.l

i.50(35) + 0.50(52) = 78.l

52.fifty + 26 = 78.50

AND

x + y = 87

35 + 52 = 87

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

That wasn't too bad, was it? The hardest role is writing the equations. From there you lot already know the strategies for solving. Recall advisedly about what'south happening in the trouble when trying to write the two equations.

Case ii: Another Word Problem

You and a friend go to Tacos Galore for dejeuner. You lot order three soft tacos and iii burritos and your total bill is $eleven.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much practise soft tacos cost? How much do burritos cost?

ane. Let's start past identifying the of import data:

iii soft tacos + iii burritos toll $11.25
four soft tacos + 2 burritos cost $10.00

two. Define your variables.

Ask yourself, "What am I trying to solve for? What don't I know?

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

Let x = the price of one soft taco

Let y = the cost of 1 burrito

3. Write two equations.

Ane equation will be related your dejeuner and 1 equation will be related to your friend's lunch.

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

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

4. Solve!

We tin can choose whatever method that we like to solve the arrangement of equations. I am going to cull the combinations method.

Solving Systems Using Combinations

v. Call up about what the solution means in context of the trouble.

ten = the cost of i soft taco and x = 1.25.

That means that 1 soft tacos costs $one.25.

y = the price of i burrito and y = 2.v.

That ways that 1 burrito costs $2.l.

Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You lot must be able to apply your noesis!

If you have difficulty with existent globe issues, you can detect more examples and do problems in the Algebra Class E-course.

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

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