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## Unit 6: Lesson 6

- Age word problem: Imran
- Age word problem: Ben & William
- Age word problem: Arman & Diya
- System of equations word problem: walk & ride
- System of equations word problem: no solution
- System of equations word problem: infinite solutions

## Systems of equations with elimination: TV & DVD

- Systems of equations with elimination: apples and oranges
- Systems of equations with substitution: coins
- Systems of equations with elimination: coffee and croissants
- Systems of equations: FAQ

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## Video transcript

## ELIMINATION METHOD WORD PROBLEMS WORKSHEET

## Detailed Answer Key

Let x be the no. of adult tickets and y be the no. of kids tickets.

According to the question, we have

Eliminate one of the variables to get the value of the other variable.

To change the sign of y in (1), multiply both sides of (1) by negative sign.

Now, eliminate the variable y in (2) and (3) as given below and find the value of x.

Substitute 202 for x in (1) to get the value of y.

So, the number of adults tickets sold is 202 and the number of kids tickets sold is 346.

Let x and "y" be the cost prices of two products.

Let us assume that x is sold at 20% profit

Then, the selling price of x is 120% of x.

Let us assume that y is sold at 20% loss

Then, the selling price of y is 80% of y.

Given : Selling price of x + Selling price of y = 52

To avoid decimal, multiply both sides by 10

In (1) and (2), both the variables x and y are not having the same coefficient.

One of the variables must have the same coefficient.

So multiply both sides of (1) by 2 to make the coefficients of y same in both the equations.

(1) ⋅ 2 --------> 2x + 2y = 100 ----------(3)

Variable y is having the same sign in both (2) and (3).

To change the sign of y in (3), multiply both sides of (3) by negative sign.

Now, eliminate the variable y in (2) and (4) as given below and find the value of x.

Substitute 30 for x in (1) to get the value of y.

So, the cost prices of two products are $30 and $20.

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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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## IMAGES

## VIDEO

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