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Solving A System of Equations

In this problem situation, Maggie buys fruit slushies for $0.75 each and conies for $1.00 each, spending a total of $12.75 for 5 items. We define variables for the number of fruit slushies (f) and conies (c) to establish a system of equations. By using the elimination method, we set up the equations: 0.75f + 1c = 12.75 and f + c = 5. Through solving, we find that the theoretical result yields negative slushies, indicating there is no real-life solution. This problem shows the importance of constraints in real-world applications.

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Solving A System of Equations

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  1. Solving A System of Equations Aileen & Ashley December 19, 2013 5-6B

  2. Problem Situation Maggie went to Hotdog World and bought fruit slushies for 75 cents each and conies for 1 dollar each. She spent a total of $12.75 and she bought 5 total items. How many fruit slushies did she buy?

  3. Define Variables • f = number of Fruit slushies • c = number of Conies

  4. System of Equations • 0.75f + 1c = 12.75 • c + f = 5

  5. Solution Method • We are going to solve this equation by the method of elimination.

  6. Step 1 of Solution .75f + 1c = 12.75 Subtract the equations. f + c = 5 -0.25f = 7.75 Divide both sides by -0.25 -0.25 -0.25 f = -31

  7. Step 2 of Solution f + c = 5 Replace f. -31 + c = 5 +31 +31 Add to both sides. c = 36

  8. Solution to the System of Equations • (c, f) (36,-31)

  9. Check of Solution • 0.75(-31) + 36 = 12.75 • -31 + 36 = 5

  10. Solution in the Problem Situation • There is no real life solution, because you can not order a negative 31 in slushies.

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