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Math 8 U4L29
Lesson 29: Word Problems Write word problems into systems of linear equations.
Solve systems of linear equations using elimination and substitution methods.
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Example 1
The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers?
1. Define Variables: x is one number, y is the other number.
2. Write an equation to represent the information in the word problem.
x + y = 361, x ­ y = 173
Two equations that represent the situation.
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3. Solve this system
4. Write your answer in a complete sentence.
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Example 2
There are 356 eighth‐grade students at Euclid’s Middle School. Thirty‐four more than four times the number of girls is equal to half the number of boys. How many boys are in eighth grade at Euclid’s Middle School? How many girls?
1. Define the variables.
x ­ # of boys, y ­ # of girls
2. Write equations.
x+y=356
34 + 4y = .5x
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3. Solve this system
4. Write your answer in a complete sentence.
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Example 3
A family member has some five‐dollar bills and one‐dollar bills in her wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have?
1. Define variables:
x: # of five dollar bills, y: # of one dollar bills
2. Write equations.
x + y = 18
5x + 1y = 62
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3. Solve this system.
4. Write your answer in a complete sentence.
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Example 4
A friend bought 2 boxes of pencils and 8 notebooks for school, and it cost him $11. He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would 7 notebooks cost?
1. Define variables:
x: cost of a box of pencils
y: cost of 1 notebook
2. Write equations
2x + 8y = 11
3x + 5y = 11.25
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Solve this system
4. Write your answer in a complete sentence.
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Closing
1. Define Variables
2. Write Equations
3. Solve the System
4. Write your answer as a complete sentence.
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Exit Ticket May 16, 2016
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When finished with the problem set.
Algebra Book, page 422­ 423, problems 47 ­ 55 all.
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