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Last day of school for this semester is Friday December 16th

Last day of school for this semester is Friday December 16th. Benchmark week is Monday 12 th – Friday 16 th is For all students missing quizzes or exams, you must make them up before FRIDAY DECEMBER 9 TH .

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Last day of school for this semester is Friday December 16th

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  1. Last day of school for this semester is Friday December 16th • Benchmark week is Monday 12th – Friday 16th is • For all students missing quizzes or exams, you must make them up before FRIDAY DECEMBER 9TH. • Re-takes will be given tomorrow after school, Thursday 8th, and Friday 9th after school.

  2. Students who currently have an NPmust come and talk to me so that we can agree on a course of action. There will be a quiz next Monday • D= rt • Mixture Problems

  3. Do now: Suppose you hike up a hill in 6 hours. You hike back down took only 3 hours at 4 km/h. Find your average speed up hill.

  4. 2.6 Mixture Problems

  5. Objectives: • To solve mixture problems • To solve real world problems involving consumer issues. Standards: • 15.0

  6. Solving Mixture Problems: • Raisins cost $2 per pound and nuts cost $5 per pound. How many pounds of each should you use to make a 30-lb mixture that costs $4 per pound?

  7. r $2 2r 30 - r $5 5(30 – r) 30 4(30) $4

  8. + = 2r + 150 – 5r = 120 -3r + 150 = 120 r = 10 lbs raisins 20 lbs Nuts -150 = -150 -3r = -30

  9. A typical mixture problem reads like this: Joe would like to mix 5 lbs of Columbian coffee costing $4.50 per pound with enough flavored coffee costing $3.00 per pound to make a mix worth $4.00 per pound. How many pounds of the flavored coffee should he take? Let x = amount of flavored coffee in pounds Mixture problems can be more easily solved by using a grid.

  10. Joe would like to mix 5 lbs of Columbian coffee costing $4.50 per pound with enough flavored coffee costing $3.00 per pound to make a mix worth $4.00 per pound. How many pounds of the flavored coffee should he take? 5 4.50 3.00 x 4.00 Let’s fill in the chart with what we know. BACK

  11. Joe would like to mix 5 lbs of Columbian coffee costing $4.50 per pound with enough flavored coffee costing $3.00 per pound to make a mix worth $4.00 per pound. How many pounds of the flavored coffee should he take? 22.5 5 4.50 + 3.00 3x x x + 5 4.00 4(x + 5) = 22.5 + 3x = 4(x + 5). BACK

  12. He will need 2.5 lbs of the flavored coffee. BACK

  13. Next Problem Extra Credit

  14. An auto mechanic has 300 mL of battery acid solution that is 60% acid. He must add water to the solution to dilute it so that it is only 45% acid. How much water should he add? 300 60% 180 0% 0 x .45(300 + x) 300 + x 45% Equation: 180 = 0.45 (300 + x) BACK

  15. Next Problem Extra Credit

  16. A chemist has one solution that is 40% acid and another solution that is 80% acid. How many liters of each solution does the chemist need to make 300 liters of a solution that is 64% acid?

  17. A chemist has one solution that is 40% acid and another solution that is 80% acid. How many liters of each solution does the chemist need to make 300 liters of a solution that is 64% acid? a 40% 0.4a + 300 - a 80% 0.8(300 – a) 300 64% 0.64(300) = 0.4a + 0.8(300 – a) = 0.64(300)

  18. A chemist has one solution that is 40% acid and another solution that is 80% acid. How many liters of each solution does the chemist need to make 300 liters of a solution that is 64% acid? 0.4a + 0.8(300 – a) = 0.64(300) 0.4a + 240 – 0.8a = 192 -240 = -240 0.4a – 0.8a = -48 -0.4a = -48 -0.4 = -0.4 a = 120 The chemist needs 120L of 40% solution and 300 – 120 = 180L of 80% solution.

  19. John has $1.70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Let d = number of dimes Let n = number of nickels Counting equation d + n = 22 Value equation .10d + .05n = 1.70 BACK

  20. -10

  21. Tickets to a movie cost $5.00 for adults and $3.00 for children. If tickets were bought for 50 people for a total of $196 how many adult tickets were sold and how many children tickets were sold? Let A = the number of Adult tickets sold. Let C = the number of children tickets sold. Counting Equation A + C = 50 Value Equation 5A + 3C = 196 BACK

  22. 23 + C = 50 A + C = 50 -3 5A + 3C = 196 C = 27 -3A – 3C = -150 23 Adults and 27 Children 2A = 46 A = 23 Check 5(23) + 3(27) = 196 115 + 81 = 196

  23. How much 20% alcohol solution and 50% alcohol solution must be mixed to get 12 gallons of 30% alcohol solution? Let x = amount of 20% Let y = amount of 50% Counting Equation x + y = 12 Value Equation .20x + .50y = .30(12) .30(12)= 3.6 BACK

  24. x + (4) = 12 x + y = 12 -2 .20x + .50y = 3.6 x = 8 10 2x + 5y = 36 8 gallons of 20% 4 gallons of 50% -2x – 2y = -24 3y = 12 y = 4 Check .2(8) + .5(4) = 3.6 1.6 + 2 = 3.6 BACK

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