1. Solving Mixture Word Problems Aug. 11 th, 2014

2. What is a solution? A solution is a mixture of one substance dissolved in another so the properties are the same throughout. For our examples we will be mixing different concentrations of solutions in order to obtain a specific concentration that we do not have.

3. Example 1 How many ounces of a 30% solution should Jane mix with 40 ounces of a 60% solution to make a 35% solution? % (in decimals)ounces.3x.3x.640.6(40).35x+40 Percentage we wish to obtain..35(x + 40) =.3x +.6(40).35x + 14 =.3x + 24 -.3x.05x + 14 = 24 -14 -14.05x = 10.05.05 x = 200 *Multiply ACROSS *Add DOWN Jane would need 200 ounces of 30% solution to make a 35% solution.

4. Example 2 If you have 20 ounces of a 50% solution, how much must you add of a 20% solution to make a 45% solution? % (in decimals)ounces.520.5(20).2x.2x.4520 + x.45(20 + x) =.5(20) +.2x 9 +.45x = 10 +.2x -.2x -.2x 9 +.25x = 10 - 9.25x = 1.25.25 x = 4 You would need 4 ounces of 20% solution to make a 45% solution.

5. Example 3 An exterminator has one tank containing a 50% water solution of poison and another tank that contains 30% solution of the same poison, How much of each solution must the worker mix to make 40 liters of a 35% solution? % (in decimals)liters.5x.5x.3y.3y.3540.35(40) =.5x +.3y 14 =.5x +.3y 14 =.5x +.3(40 – x) 14 =.5x + 12 -.3x 14 =.2x + 12 - 12 - 12 2 =.2x.2.2 How much he wants to make total. x + y = 40 -x y = 40 - x We now have 2 variables, so we need 2 equations. Solve for a variable Substitute to make a 1 variable equation x = 10

6. What does that mean? You need 10 liters of 50% solution. But what about the 30% solution? Plug in 10 for x! You need 30 liters of the 30% solution. So all together: The worker needs 10 liters of 50% solution and 30 liters of 30% solution. y = 40 - x y = 40 – 10 y = 30

7. Real Word Problems

8. Example 4 If Jim can paint a house in 6 hours and James can paint the same house in 7 hours, how long will it take for them to paint to paint the house together? Set up ratios Find the common denominator Simplify Solve H = 3.23 It would take them 3.23 hours to paint the house together.

9. Example 5 If Jasmine can detail a car in 3 hours and Carlos can detail the same type of car in 5 hours, how long will it take for them to detail the car together? Set up ratios Find the common denominator Simplify Solve C = 1.875 It would take them 1.875 hours to paint the house together.