Math, Lecture Notes

Section 7.3 Problem 1 (6A, Practice 4B, p54) Part (a): 9% of 125 = (0.09)(125) = 11.25 Part (b): 78% of 900 = (0.78)(900) = 702 Part (c): 30% of 8250 = (0.3)(250) = 875 Part (d): 457% of 400m = (0.45)(400) = 180 m Part (e): 21% of 50 l = (0.21)(50) = 10.5 l Part (f): 169% of 60 kg = (0.16)(60) = 9.6 kg Problem 2: 4% of $1500 = (0.04)(1500) = $60 Problem 3: 40% of 15 = (0.4)(15) = 6 arrows hit the target Alternative: 40% of arrows hit, 60% of arrows did not hit; 60% of 15 = (0.6)(15) = 9 Problem 4: 64% are air-conditioned, 36% are not air-conditioned 36% of 125 = (0.36)(125) = 45 are not air-conditioned Problem 5: 5% discount on $200 = (0.05)(200) = $10 discount; so selling price = $200 - $10 = $190 Alternative: 5% discount, selling price is 95% of 200; (0.95)(200) = $190 Problem 6: 5% of $1400 = (0.05)(1400) = $70 So his monthly salary after the increase = $1400 + $70 = $1470 Alternative: His monthly salary after the increase = 105% of $1400 = (1.05)(1400) = $1470 Problem 7: OK to add percentages here since of the same quantity. 60% + 24% = 84% 16% of the stamps are European 16% of 300 = (0.16)(300) = 48 European stamps Problem 8: After making the meatballs, She has 1600g - 350g = 1250g left. She used 80% of the remainder for hamburgers. So she'll have 20% of 1250g left; (0.2)(1250) = 250g left Problem 9: She spent 15% of $80 or (0.15)(80) = $12 on vegetables She has $80 - $12 = $68 remaining She spent 50% of $68 or (1/2)(68) = $34 on meat Problem 10: 60% of the class are girls, so 40% are boys (0.6)(40) = 24 girls, so 40 - 24 = 16 boys 50% of the girls wear glasses; so (1/2)(24) = 12 girls wear glasses 25% of the boys wear glasses; so (1/4)(16) = 4 boys wear glasses So 12 + 4 = 16 students wear glasses Alternative: 60% of 40 = (1/2)(40) = 20 girls wear glasses 25% of 40 = (1/4)(40) = 10 boys wear glasses So 20 + 10 = 30 students wear glasses Problem 2: Let x = original price $26 is 65% of x So 0.65x = 26 x = 26 / 0.65 = 40 The original price of the shirt was $40 Problem 3: Whole Unit = usual price of the bicycle Discount of 15% means 85% of usual price Let x = usual price $340 is 85% of x 0.85x = 340 x = 340 / 0.85 = 400 The usual price is $400 Problem 4: Whole Unit = English test score Let x = English test score 84 is 105% of x 1.05x = 84 x = 84 / 1.05 = 80 She scored 80 on her English test Problem 5: Whole Unit = amount spent last week Let x = amount spent last week $55 is 110% of x 1.1x = 55 x = 55 / 1.1 = 50 He spent $50 last week Image Analysis Problem 4(a): Exercise 3.5: If a price is reduced by 20% and then the sale price is reduced by 30%, what percent is the overall reduction? You are paying 70% of 80% of the original price.   (0.7)(0.8) = 0.56 You pay 56% of the original price; the overall reduction is 44% of the original price. Problem 4(b): Let x = monthly salary 20% of x is $240 0.2x = 240 x = 240 / 0.2 = 1200 Problem 5: Let x = number of books 280 is 35% of x 0.35x = 280 x = 280 / 0.35 = 800 Problem 6: Let x = usual price of dress 25% of x is $15 0.25x = 15 x = 15 / 0.25 = 60 Problem 5: (6A, Practice 4E, p68) Part (a): 1.5 kg = 1500 g 40% of 1500 = 600 60% of 1500 = 900 There are 24 boys Part (b): Let x = supervisor's pay $1500 is 80% of x 0.8x = 1500 x = 1500 / 0.8 = 1875 Part (c): Discount of 10% means pay 90% of usual price Let x = usual price $45 is 90% of x 0.9x = 45 x = 45 / 0.9 = 50 Part (d): Tim answered 80% of 50 or (0.8)(50) = 40 questions Carlos answered 90% of 50 or (0.9)(50) = 45 questions Carlos answered 5 more questions correctly than Tim 5 is what percent of 40? 5/40 = 1/8 = 12.5% Part (e): 60% of 200 = (0.6)(200) = 120 males 200 - 120 = 80 females There are 40 more males than females Express the difference as a percentage of the number of females: 40/80 = 1/2 = 50%   Part (f): First 40% of beads are red So 60% of beads are yellow 60% of 180 = (0.6)(180) = 108 yellow beads 108 + 80 = 188 beads altogether