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. Mixtures 1st solution2nd solution3rd solution += x ozy oz60 oz How many ounces are there in each solution?

5. Mixtures 1st solution2nd solution3rd solution += x ozy oz60 oz How much acid is there in each solution? 15% Acid 40% Acid 25% Acid

6. Mixtures Lets now make a table…. 1st solution2nd solution3rd solution += x ozy oz60 oz 15% Acid 40% Acid 25% Acid

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

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

9. Mixtures % ACID Amount of solution Amount of Acid 1st Solution 2nd Solution 3rd Solution 15% 40% 25% x y 60 0.15x 0.40y 0.25(60) xy60+= +=0.15x0.40y0.25(60) x = 36 y = 24

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

12. Mixtures % alcohol Amount of antifreeze Amount of alcohol 1st Antifreeze 2nd Antifreeze Total Antifreeze 40% 60% 48% x y 1000 0.40x 0.60y 0.48(1000) xy1000+= +=0.40x0.60y0.48(1000) x = 600 y = 400

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 % Copper Amount of Alloy Amount of Copper 1st Alloy 2nd Alloy Total Alloy 25% 50% 45% x y 100 0.25x 0.50y 0.45(100) xy100+= +=0.25x0.50y0.45(100) x = 20 y = 80

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 $$$ Type of Coin Number of coins Value of Coin Value in Cents Quarters Dimes Total q d 250 $0.25 $0.10 0.25q 0.10d $39.25 qd250+= +=0.25q0.10d39.25q = 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 $$$ Type of Coin Number of coins Value of Coin Value in Cents Nickels Dimes Total n d 83 $0.05 $0.10 0.05n 0.10d $6.95 nd83+= +=0.05n0.10d$6.95n = 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 $$$ Type of Coin Number of coins Value of Coin Value in Cents Quarters Half Dollars Total q h 70 $0.25 $0.50 0.25q 0.50h $24.25 qh70+= +=0.25n0.50d$24.25q = 27 h = 43