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Solving Problems With Algebra

Solving Problems With Algebra . Algebra One Ms. Hardy. EXAMPLE ONE: You and two friends go to the movie theater. You each buy a popcorn for $7 and a soda for $5.75 and the movie ticket. The total cost for the three of you was $69.75. How much does a movie ticket cost?

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Solving Problems With Algebra

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  1. Solving Problems With Algebra Algebra One Ms. Hardy

  2. EXAMPLE ONE: You and two friends go to the movie theater. You each buy a popcorn for $7 and a soda for $5.75 and the movie ticket. The total cost for the three of you was $69.75. How much does a movie ticket cost? • What is the unknown in the problem? Assign it a variable. • Write an expression for the cost for one person. • Write an expression for the total cost for everyone. • Write an equation showing this equals a total cost of $69.75.

  3. EXAMPLE TWO: You are helping to make pies for Thanksgiving for the local soup kitchen. You start peeling apples. Four minutes later your best friend joins you and starts peeling apples. There are several variable quantities in this problem. What are they? • Number of minutes you peeled apples • Number of minutes your friend peeled apples • Number of apples you peeled. • Number of apples your friend peeled. • Total number of apples peeled.

  4. Suppose you start peeling apples at the rate of 3 apples per minute. Four minutes later your best friend arrives and peels at the rate of 5 apples per minute. • Define a variable for the number of minutes you’ve been peeling. • Write expressions for • Number of minutes your friend has been peeling. • Number of apples you peeled. • Number of apples your friend peeled. • The total number of apples peeled.

  5. Write an equation stating that you have together peeled 36 apples. • Now solve the equation to find out how long you peeled apples. • How long did your friend peel apples? • How many apples did you peel? • How many apples did your friend peel? • Do these answers make sense? Tell me how you know.

  6. Arithmetic Sequences Revisited Let’s revisit the toothpick problem from Unit 1. If we had a box of 100 toothpicks, how many connected pentagons could we build?

  7. If we had a box of 100 toothpicks, how many connected pentagons could we build? The formula to find the nth term of an arithmetic sequence is an = a + (n – 1)d What do you think the different variables represent in this formula?

  8. If we had a box of 100 toothpicks, how many connected pentagons could we build? an = a + (n – 1)d 23 connected pentagons – this uses only 97 but you don’t have enough to make another one.

  9. Arithmetic Sequences Revisited ANOTHER EXAMPLE During spring training, a major league baseball team has their pitcher increase the number of pitches he throes every time he starts, He started with 25 pitches in the first game and added the same number of pitches each time. Now after 9 games, he is up to 81 pitches. What is the number of new pitches that is added to each successive game? 7 new pitches per game

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