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Solving Systems of Equations

Solving Systems of Equations. Classic Applications (Mixture & Money). Objectives. Identify the givens of a problem Organize a data table to create a system Use table to find a system of equations SOLVE!!!!. :-). Mixtures. How many ounces of a 15% acid solution

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Solving Systems of Equations

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  1. Solving Systems of Equations Classic Applications (Mixture & Money)

  2. Objectives • Identify the givens of a problem • Organize a data table to create a system • Use table to find a system of equations • SOLVE!!!! :-)

  3. Mixtures How many ounces of a 15% acid solution should be mixed with a 40% acid solution to produce 60 ounces of a 25% solution? Hmmmmm……

  4. 1st solution 2nd solution 3rd solution Mixtures + = x oz y oz 60 oz How many ounces are there in each solution?

  5. 1st solution 2nd solution 3rd solution Mixtures 25% Acid 40% Acid 15% Acid + = x oz y oz 60 oz How much acid is there in each solution?

  6. 25% Acid 40% Acid 15% Acid + = x oz y oz 60 oz 1st solution 2nd solution 3rd solution Mixtures Lets now make a table….

  7. Mixtures Amount of solution Amount of Acid % ACID 15% x 0.15x 1st Solution 40% y 2nd Solution 0.40y 3rd Solution 25% 60 0.25(60) REMEMBER: 1st Solution + 2nd Solution = 3rd Solution

  8. Mixtures Amount of solution Amount of Acid % ACID 15% x 0.15x 1st Solution 40% y 2nd Solution 0.40y 3rd Solution 25% 60 0.25(60) Use the table to write our two equations….

  9. Mixtures Amount of solution Amount of Acid % ACID 15% x 0.15x 1st Solution 40% y 2nd Solution 0.40y 3rd Solution 25% 60 0.25(60) x + y = 60 x = 36 y = 24 0.15x + 0.40y = 0.25(60)

  10. Mixtures A gas station attendant has some antifreeze that is 40% alcohol and another type of antifreeze that is 60% alcohol. He wants to make 1,000 gallons of antifreeze that is 48% alcohol. How much of each kind should he use?

  11. Mixtures Amount of antifreeze Amount of alcohol % alcohol 40% x 0.40x 1st Antifreeze 60% y 2nd Antifreeze 0.60y Total Antifreeze 48% 1000 0.48(1000) Use the table to write our two equations.

  12. Amount of antifreeze Amount of alcohol % alcohol 40% x 0.40x 1st Antifreeze 60% y 2nd Antifreeze 0.60y Total Antifreeze 48% 1000 0.48(1000) Mixtures x + y = 1000 x = 600 y = 400 0.40x + 0.60y = 0.48(1000)

  13. You Try a Mixture A metal alloy is 25% copper. Another is 50% copper. How much of each alloy should be used to make 100 grams of an alloy that is 45% copper

  14. You Try a Mixture Amount of Alloy Amount of Copper % Copper 25% x 0.25x 1st Alloy 50% y 2nd Alloy 0.50y Total Alloy 45% 100 0.45(100) x + y = 100 x = 20 y = 80 0.25x + 0.50y = 0.45(100)

  15. Money $$$ In a coin bank there are 250 dimes and quarters worth a total of $39.25. Find how many of each kind of coin are in the bank…

  16. Money $$$ Number of coins Value in Cents Type of Coin Value of Coin Quarters q $0.25 0.25q $0.10 Dimes d 0.10d 250 $39.25 Total q + d = 250 0.25q + 0.10d = 39.25 q = 95 d = 155

  17. Money $$$ Omar broke open his “piggy bank” and found 83 coins in nickels and dimes. If he had $6.95 in all, how many coins of each does he have?

  18. Money $$$ Number of coins Value in Cents Type of Coin Value of Coin Nickels n $0.05 0.05n $0.10 Dimes d 0.10d 83 $6.95 Total n + d = 83 0.05n + 0.10d = $6.95 n = 27 d = 56

  19. Money $$$ Mr. Garza was cleaning his book shelf when he suddenly tipped over and broke his precious “turtle bank.” To his discovery he counted 70 coins of quarters and half dollars totaling to $24.25. How many quarters and half dollars did Mr.Garza have?

  20. Money $$$ Number of coins Value in Cents Type of Coin Value of Coin Quarters q $0.25 0.25q $0.50 Half Dollars h 0.50h 70 $24.25 Total q + h = 70 0.25n + 0.50d = $24.25 q = 27 h = 43

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