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Real World Applications

Explore real-life scenarios through solving systems of equations and inequalities using various methods like graphing, substitution, and elimination. Practice with engaging examples and guided exercises for hands-on learning.

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Real World Applications

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  1. Real World Applications System of equations System of Inequalities

  2. Warm Up: Solve each system • Graphing: • Y = 2/3x + 4 • Y = 2x - 3 • Substitution • 3x – 4y = -5 • Y = 5x -3 • Elimination • 3x + 2y = 1 • X - 4y =-9 • System of Inequalities:

  3. Homework Questions:

  4. Hint: • Remember when a total is given the equation will be in standard form • When total is missing it is an equation in slope intercept form • Your unit of measurements always go together • Example: money money MUST be with money

  5. Let try some real world application: • Define your variables • Set up each equation • Solve using the best method • Answer what is ask.

  6. Handout • Cut each equation • Glue them in the order that you cut. • MUST leave room to workout problem.

  7. Example 1: • A-Tunes requires a membership fee of $12 a month and $1 for each download. Bapstar requires a membership fee of $5 a month but charges $1.50 for each download. When do the charges for the two companies equal each other?

  8. Example 2: • Rent-A-SUV charges $100 fee to rent a truck and $12 per mile. Mavis Rental Company charges a $150 fee to rent a truck and $8.50 per mile. When do the two rental companies equal? If you are taking a trip that requires you to drive 150 miles, which company should you choose?

  9. Example 3: • Beth bought 3 apples and 2 oranges at the local market for $3.90. The next day she bought 5 apples and 3 oranges and paid $6.30. How much does each apple and each orange cost?

  10. Example 4: • The senior class wants to raise money for the senior gift by selling T-shirts. They must pay a $250 set up fee to get the t-shirts printed. Each shirt will cost them $3.00. If they sell the t-shirts for $8 each, how many shirts must they sell to raise $2,000?

  11. Take out yesterday’s guided note: • What would a real world application of an inequalities system look like?

  12. Real world applications: • The SAT has two parts, math and verbal. The maximum score is 1600. For admission to the school of your choice, you need at least a 600 in math. Write a system of inequalities to model the situation.

  13. Real world applications: • A psychologist needs at least 40 subjects for her experiment. She cannot use more than 30 children. Write a system of inequalities to model the situation.

  14. Real world applications: • Suppose you are buying two kinds of notebooks for school. A spiral notebook costs $2, and a three-ring notebook costs $5. You must have at least six notebooks. The cost of the notebooks can be no more than $20. Write a system of inequalities to model the situation.

  15. Real world applications: • A camp counselor needs not more than 30 campers to sign up for two mountain hikes. The counselor needs at least 10 campers on the low trail and at least 5 campers on the high trail. Write a system of inequalities to model the situation.

  16. Let write some Journal: • Finish for homework

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