Name: Class: Date: ID: A Chapter 8 Review - Solving Equations 1 A bag of marbles contains 36 red marbles There are one quarter as many purple marbles as there are red ones There are 3 times as many green marbles as there are purple ones Determine the number of green marbles in the bag 2 At a school dance, the student council sold cans of pop and bags of chips The price of a can of pop is one and a half times the price of a bag of chips The pop sells for $090 and they sold $28800 worth of pop The number of bags of chips sold is three quarters of the number of cans of pop sold What was the income from the chips? 1
Name: ID: A 3 Susan charges a flat rate of $20 per night of babysitting She also charges an extra fee of $3 per hour for every hour she works past 8 pm If Susan received $32 for a night of babysitting, how late did she work? 4 During a ski jump, Maiko is airborne for 81 s If her speed during the jump is 276 m/s, how far did Maiko jump, to the nearest hundredth of a metre? 5 The annual rainfall in Winnipeg is 9 mm more than 1 1 times the annual rainfall in Calgary If the annual 3 rainfall in Winnipeg is 4156 mm, what is the annual rainfall in Calgary, to the nearest hundredth of a millimetre? 2
Name: ID: A 6 The bill for 6 hockey tickets was $39000 This included a handling charge of $500 for each ticket What was the base price for each ticket with no handling fee? 7 A local tour company is offering a weekend travel package special at 30% off the regular price This is a savings of $8745 What is the regular price of the package? 8 A bulk-food store sells a variety of nuts James buys 0325 kg of almonds and 0735 kg of peanuts Almonds cost $085 for 100 g If James spends a total of $835 on nuts, what is the price of 100 g of peanuts? Round your answer to the nearest cent 3
Name: ID: A 9 A skier takes 2 min and 24 s to complete a run of 18 km Determine the average speed of the skier, in m/s 10 The length of the swimming pool at the Gordon Recreation Centre is 33 m less than the length of the pool at the Cedar Aquatic Centre John can swim 18 lengths of the pool at the Gordon Recreation Centre If John swims the same number of lengths of the Cedar Aquatic Centre pool, how many additional metres does he swim? 4
Chapter 8 Review - Solving Equations Answer Section SHORT ANSWER 1 ANS: Example: Ê g = 3 r ˆ Ë Á 4 Ê g = 3 36 ˆ Ë Á 4 g = 3(9) g = 27 There are 27 green marbles in the bag PTS: 1 DIF: Average OBJ: Section 81 NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: one-step equation division multiplication 2 ANS: Example: Pop sold = 28800 090 = 320 cans Bags of chips sold = 3 4 320 = 240 Value of chips sold = 240 060 = $14400 The student council sold $14400 worth of chips PTS: 1 DIF: Difficult OBJ: Section 82 NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation variable 1
PROBLEM 3 ANS: Let h represent the number of hours past 8 pm that Susan worked 32 = 20 + 3h 32 20 = 3h 12 = 3h 4 = h 4 hours past 8 pm is 12 am Susan worked until midnight PTS: 1 DIF: Difficult OBJ: Section 82 NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation subtraction division money problem solving 4 ANS: Let d represent the distance of Maiko s ski jump d = 276 81 d = 22356 The distance of Maiko s ski jump was 22356 m PTS: 1 DIF: Average OBJ: Section 81 NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: one-step equation speed distance problem solving 5 ANS: Let c represent the annual rainfall of Calgary 4156 = 9 + 1 1 3 c 4066 = 1 1 3 c 30495 = c The annual rainfall of Calgary is 30495 mm PTS: 1 DIF: Difficult OBJ: Section 82 NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation subtraction division problem solving 2
6 ANS: Example: Let t represent the base price of one hockey ticket 6t + 6 500 = 390 6t + 3000 = 390 6t = 390 30 t = 360 6 t = 60 Each ticket has a base price of $6000 PTS: 1 DIF: Average OBJ: Section 83 NAT: PR3 TOP: Solving Equations: a(x + b) = c KEY: multi-step equation subtraction division money problem solving 7 ANS: Example: Let p represent the regular price of the package 30 100 = 8745 p 30p = 8745 p = 29150 The regular price of the package is $29150 Check: 29150 03 = 8745 30% of $29150 is $8745 My answer is correct PTS: 1 DIF: Difficult+ OBJ: Section 81 NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: multi-step equation multiplication division money problem solving 3
8 ANS: Convert kilograms to grams 1 kg = 1000 g 0325 kg = 325 g 0735 kg = 735 g Find the number of 100-g portions in each amount of nuts 325 g 100 g = 325 735 g 100 g = 735 Let p represent the price of 100 g of peanuts 835 = (085 325) + (p 735) 835 = 27625 + 735p 835 27625 = 735p 55875 = 735p 07602 = p p = 076 The cost of 100 g of peanuts is $076 PTS: 1 DIF: Difficult+ OBJ: Section 83 NAT: PR3 TOP: Solving Equations: a(x + b) = c KEY: multi-step equation subtraction division money problem solving 9 ANS: 18 km = 18 1000 = 1800 m 2 min24 s = 2(60) + 24 = 144 s Let s represent the speed of the skier s = distance time s = 1800 144 s = 125 m/s The average speed of the skier is 125 m/s PTS: 1 DIF: Difficult+ OBJ: Section 81 NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: single-step equation speed problem solving 4
10 ANS: Let m represent the number of additional metres swum by John at the Cedar Aquatic Centre pool m = 18(33) m = 594 John swims an additional 594 m PTS: 1 DIF: Average OBJ: Section 82 NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: one-step equation multiplication distance problem solving 5