1. Mixture Problems CST review 4A: #5 CST review 4B: #5 Other problems CST review 4C: #17

2. 60% acid sol 0% acid sol Water 45% acid sol Total ml300 mlx ml(300 + x) ml ml of acid(.60)3000.45(300 + x) -135 = -135 x = 100 ml of water CST 4A, #5 The mechanic has 300 mL of battery acid solution that is 60% acid. He must add water to this solution to dilute it so that it is only 45% acid. How much water should be added?.60(300) + 0 =.45(300 + x) 180 = 135 +.45x 45 =.45x

3. 70% alcohol sol40% alchl sol50% alchl sol Total litersx liters50 liters(x + 50) liters liters of acid.70x.40(50).50(x + 50) Total sol = x + 50.70x +.40(50) =.50(x + 50).70x + 20=.50x + 25.20x = 5 20x = 500 x = 25 CST 4B, #5 How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

4. Peanuts ($3.50)Almnd ($4.75)$4.00 mixed nuts Total amtx lbsy lbs20 lbs cost3.50x4.75y4(x + y) A health food store sells a mixture of peanuts and roasted almonds. Peanuts sell for $3.50/lb and almonds sell for $4.75/lb. How many pounds of each should be mixed to make 20 lbs. of this snack worth $4.00/lb.? x + y = 20 3.50x + 4.75y = 4(x + y) 3.50x + 4.75y= 4x + 4y.5x =.75y 50(20 - y) = 75y y = 8 CST 4C, #6 x = 20 - y 1000 - 50y = 75y 1000 = 125y 50x = 75y x = 20 - 8 x = 12 12 lb peanuts 8 lb almonds

5. CST 4C, #17 14 20 x x 160 cm 2 A picture frame measures 20 cm by 14 cm. The picture, inside the frame, takes up 160 square centimeters. Find the width of the frame. (20 – 2x)(14 – 2x) = 160 x x 14 – 2x 20 – 2x 280 – 68x + 4x 2 = 160 4x 2 - 68x + 280 = 160 4x 2 - 68x + 120 = 0 4(x 2 - 17x + 30) = 0 4(x - 15)(x - 2) = 0 x = 15, 2 x can’t be 15x = 2 14 – 2x = 14 – 2(2) = 10 Width is 10, length is 20 – 2x = 20 – 2(2) =16