Percent Mixture Problems Written by Dr. Ed D’Souza, Rialto Unified School District Using the tug-of-war approach, imagine the white jelly beans having a tug-of-war game with the blue jelly beans. Both want the final price to be closer to their price. METHOD 2:Teeter-Totter Method White jelly beans cost $0.25 a pound and blue jelly beans cost $0.85 a pound. How many pounds of white jelly beans must be added to 25 pounds of blue jelly beans to arrive at a mixture worth $0.45 a pound? 1. Draw a "rope" (straight line) and label the three numbers you know. W=25 M =45 B= 85 2. The left point on the rope is the price of the white jelly beans (25), the right point is the price of the blue jelly beans (85), and the "fulcrum" will be located at the final price (45), and closer to the left side. Try to approximate where 45 would land between 25 and 85. Price (cents) W= 25 M= 45 B= 85 3. Label what you know - the pull to the right is 25. Label what you don't know the pull to the left is x. 4. Amount (lbs) Price(cents) Amount (lbs) 20 W= 25 x 40 M=45 B= 85 25 5. Calculate the gap in price between the knot and the left side (20cents) and between the knot and the right side (40 cents- see bullet 3.). Since the gap on the left is half as big, the left side must be pulling twice as hard. Therefore, we must have 50 pounds of white jelly beans. Students will eventually discover the rule: (gap) x (pull) = (gap) x (pull). Multiply the gap on the left (20) by the pull to the left (the unknown). Set this quantity to the gap on the right (40) times the pull to the right (25). Solving for the unknown yields 50 pounds. (20)(x) = (40)(25) x = (40)(25) = 50lbs 20 So , 50 lbs of white jelly beans need to be added to the mixture. Mixtures –Finding the Balance 1. Coffee Cost $3/lb $3.25/lb $3.50/lb Mixture 5lbs x lbs 2. Butterfat % 2% 6.4% 8.4% Mixture x liters 3. 1 liter Grape juice % 15% 20% 100% Mixture 800ml x mL MIXTURE PROBLEMS THE JELLY BEAN PROBLEM White jelly beans cost $0.25 a pound and blue jelly beans cost $0.85 a pound. How many pounds of white jelly beans must be added to 25 pounds of blue jelly beans to arrive at a mixture worth $0.45 a pound? SALT SOLUTION A mixture containing 6% salt is to be mixed with 2 ounces of a mixture which is 15% salt, in obtaining a solution which is 12% salt. How much of the first solution must be used? A SOLUTION How many liters of a 70% acid solution must be added to 50 liters of a 40% acid solution to produce a 50% acid solution? COFFEE ANYONE? Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound. A VEGETABLE MEDLEY How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 pounds of corn that costs $0.50 per pound to make a mixture of vegetables that costs $0.65 per pound? A LITE PUNCH Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 L of another punch. The resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch. THE CEREAL PROBLEM Ten grams of sugar are added to a 40-g serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture? How many liters of water must be added to 50 L of 30% acid solution in order to produce a 20% acid solution?
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