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## 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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## 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 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

## Want to join the conversation?

## Video transcript

## 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

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