Section 8.1 Extra Practice

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1 Name: Section 8. Extra Practice Date:. BLM Solve each equation. Use a number line. a) c x b) 4 4. Solve each equation. Use models of your choice to represent the solutions. a) x 0.6 b) x. Solve each equation algebraically. a) m x b) c) 4.x. 4. Solve each equation. Show a check of each solution. x a) 4x 4.96 b). c) 07. m x d) 74. e) 4m 0 4 f). 6 m. Solve each problem. a) Carol gave a % deposit on a diamond bracelet. The deposit was $7.0. What was the cost of the bracelet? b) Eric earned of the profits of the canteen on the weekend. His earnings were $60. What was the total profit earned in the canteen? c) The density of an object is determined by the formula d m, where m is v the mass, in grams, and v is the volume, in litres. What volume does the object occupy if an 8.8-g object has a density of. g/l? d) Jamal received a 0% discount when he purchased his computer. He paid $90. What was the regular price of the computer? Copyright McGraw-Hill Ryerson, 009

2 Name: Section 8. Extra Practice Date:. BLM Solve each equation. Use each of the following once: an algebraic method, a diagram, and concrete materials. a) x + b) m c) 4x Solve each equation. Then, check your answer. a) m + b) 7 n x + c) x d) e) 4c + 4. f) x Create an equation for each of the following. Solve. Then, check. a) When a number is tripled, then increased by, the result is 8. Find the number. b) Jane spent $4 for shoes. This was $4 less than twice what she spent for a blouse. How much was the blouse? c) The sum of two consecutive numbers is 7. What are the numbers? d) The cost of a banquet at Nick s Catering is $ plus $7.0 per person. If the total cost of a banquet was $87.0, how many people were invited? e) Effie and Kirsten live.6 km apart. They decided to cycle to the pool at the park, which is located between their homes. If Jennifer lives. km closer to the park, how far did they each cycle? f) Hyan has saved $00 more than two-thirds of the cost of the down payment on a car. If he has $40 saved, how much is the down payment? Copyright McGraw-Hill Ryerson, 009

3 Name: Section 8. Extra Practice Date:. BLM Show a check for each of the following. a) (x ) 8 b) 0.(x + ).4 c) x + x 4 x x. Identify the error in each of the following. Then, write the correct solution. a) 0.4(x +.).4 x + b) x +..4 x x. x x 8 x 7 7. Solve and check each of the following. a) (x 4) b) (m + 0.). c).(x +.).4 x + 4 x 7 d) ( x 8) 7 e) f) Solve. a) The perimeter of a square is 49. cm. The side length of the square is represented by the expression (x + 4.) cm. What is the value of x? b) A fraction has a denominator of 0. The numerator has a value of x less than the denominator. If the fraction is equivalent to, what is the value 4 of x? c) Two cars leave Calgary at the same time, travelling in opposite directions. Their average speeds differ by km/h. After h, they are 0 km apart. Find the speed of each car. d) A number, plus one-third of itself, plus one-eighth of itself, equals 70. What is the number? Copyright McGraw-Hill Ryerson, 009

4 Name: Section 8.4 Extra Practice Date:. BLM 8.. Solve and check each of the following. a) 0.4x.8 0.x b) 7. +.x.x x 9 x c) 6 d) 7 m m+ x e) 0 f).4m.m 0.7. Solve and check each of the following. a) x x b).m m +.8 c) n 6.4 n +.6 d) n 4+ n e) x+ x x f).m m. Solve and check each of the following. a) ( m + ) ( m ) b) 0.(x ). 0.04(x + ) c) (x +.) 4(x.) 4m + m d) 4. Create an equation for each of the following. Solve your equation. Then, check your solution. a) The length of a rectangular garden is m more than three times the garden s width. If the perimeter of the garden is 4 m, find its dimensions. b) The cash register in the school canteen contains x quarters and (0 x) dimes. If the total value of the coins is $.8, how many of each kind of coin are there? c) An employee mixes peanuts worth $.80/kg with cashews worth $.60/kg. She sells the mixture for $./kg. If she has 7 kg of peanuts, how many kilograms of cashews does she need? d) Plane A leaves the airport. One hour later, Plane B leaves the same airport on the same course. It catches up to Plane A in h. The average speed of Plane B is 00 km/h faster than Plane A. Find the speed of each plane. Copyright McGraw-Hill Ryerson, 009

Chapter 8 BLM Answers. BLM 8 6. BLM 8 Chapter 8 Math Link Introduction a) 0; 0;

a) x + 7, so x b) x 4, so x 4. a) r 4 b) s 6 c) p 4 d) x 8. a) ( 4) + 7, so x 4 is the solution b) (4) 8, so x 4 is not the solution 6.

9. y. 6. 0, or 7. or 8. 7.6 4 4 9. 8 0. $0.00 Section 8. 4. or. Example: 0.0d, so d 0.. x 4.. x 40 6. 7. 6x 8. 0 9. 0. 8 x + Section 8.4. a) x 4 b) x 8. n 0.47. x 4 4. x 7. $.0 6. x 6 7. 4 p 8. x + 9.

5 Chapter 8 BLM Answers. BLM 8 6. BLM 8 Chapter 8 Math Link Introduction a) 0; 0;, so g b) 94; h w, s so (47) 94 c) %, or 0.; 0.., 80 so s 0 d) p + b; p +, so p e) 0 b + a; b , so b 40 f) p ; ( ) p a + y ; (a + 7), so a BLM 8 Chapter 8 Get Ready. a) b) c). a) x 6 6 b) 6 x 9. a) x + 7, so x b) x 4, so x 4. a) r 4 b) s 6 c) p 4 d) x 8. a) ( 4) + 7, so x 4 is the solution b) (4) 8, so x 4 is not the solution 6. a) x 7; Check: 7 b) t ; Check: () c) g ; Check: ( ) 7 BLM 8 Chapter 8 Warm-Up Section 8.. x. x or.x. y 4. 6x + xy x 7 6. x cm 0. $4.0 Section 8.. x. 8x + xy. x 6 or 4. m.9. y. 6. 0, or 7. or $0.00 Section or. Example: 0.0d, so d 0.. x 4.. x x x + Section 8.4. a) x 4 b) x 8. n x 4 4. x 7. $.0 6. x p 8. x x x + 7 BLM 8 4 Chapter 8 Problems of the Week. 0 dimes, 0 nickels, and 80 pennies. Let x number of dimes. 0x + 0x + 8x 80, therefore, x 0.. d vt, d v t, d v t, v t + v t 00, 00t + 0t 00, 0t 00. t 00/0 hours, or / of an hour, or 40 min. They will meet 40 min after they leave.. 4, a, 4 + a, 4 + a, 8 + a, + a, 6 6 (8 + a) + ( + a) a 4 8a. a 4. (67x + 49y) + (49x + 67y) x y x + y (67x + 49y) (49x + 67y) x + ( 0y) 0 x y x + y ( + y) + y y 4 y x x Therefore, x and y. Copyright McGraw-Hill Ryerson, 009

6 . BLM 8 6. (continued) BLM 8 6 Section 8. Extra Practice. a) The diagram shows that b) The diagram shows that x. 4 8 c, or c.. a) x 0. b) x 4 0. a) x b) m, or c) x a) x.4 Left Side 4x Right Side (.4) 4.96 Left side Right side b) x.47 x Left Side Right Side Left side Right side c) m Left Side Right Side m Left side Right side d) x 7.0 Left side 7.0 Right side Left side Right side e) m 6 Left side Left side Right side f) m 84 Left side Right side 0 Right side 4 m Left side Right side. a) The bracelet cost $490. b) The canteen earned a $0 profit. c) The object has a volume of.6 L. d) The regular price of the computer was $0. BLM 8 7 Section 8. Math Link a) division; f. or f 0.4 g b) 0.4 g; 0.4n, n 0 c) I 0.4n; for eight figs, I 0.4(8), I. g d).8 0.4n, so n 4.. BLM 8 8 Section 8. Extra Practice. a) x 8 b) m.7 c) x 9. a) m 4 ; + ; 4 4 ; b) x ; ; ; ; c) n.0; ; ; d) x.4; ; ; e) c ; 4 + ; ; 6 6 f) x 8; 9. 0.( 8) +.4; ; a) x + 8. The number is. b) x 4 4. The blouse was $8. c) x + 7. The two consecutive numbers are 8 and 9. d) 7.0x They invited 9 people to the banquet. e) x Effie cycled 9. km and Kirsten cycled 4.4 km. Copyright McGraw-Hill Ryerson, 009

7 . BLM 8 6. (continued) f) x The down payment is $40. BLM 8 9 Section 8. Math Link a) 4r b) 4r 0., so r 0.0 g. c) Example: x x a) x 0 b) m. c) x 0.7 d) x 8 e) x 4 f) x 6 4. a) The value of x is 8. cm. b) The value of x is. c) 0 km/h and km/h d) The number is 48. d) Example: The algebraic method because it is quicker. BLM 8-0 Section 8. Extra Practice. a) x Left Side ( ) Right Side 8 8 Left side Right Side b) x 4 Left Side 0.(4 + ) Right Side.4 0.(7).4 Left side Right side c) x Left Side Right Side BLM 8 Section 8. Math Link a) 0.7 mg (half of the total in two servings) b) 0. mg. c) c d) c 0.6 mg e) Examples:.4 (c + 0.); c 0.6 mg BLM 8 Section 8.4 Extra Practice. a) x 9. Left Side 0.4(9.) Right Side.8 0.(9.) Left side Right side b) x 8 Left Side 7. +.(8) Right Side.(8) Left side Right side c) x 9 Left Side 9 9 ( 9) Right Side Left side Right side. a) The error is that the 0.4 was not distributed into the entire bracket. 0.4(x +.) x x 4. x. b) The error is that only one side was multiplied by. x x x + 7 x Left side Right side d) m 4 Left Side (4) 4 Left side Right side e) x Left Side 0 0 Left side Right side Right Side Right Side 0 Copyright McGraw-Hill Ryerson, 009

8 . BLM 8 6. (continued) f) m.7 Left Side.4(.7) Right Side.(.7) Left side Right side. a) x 7 Left Side (7) Right Side (7) Left side Right side b) x 6.7 Left Side Right Side.(6.7) (6.7) Left side Right side c) n 4. Left Side (4.) 6.4 Right Side (4.) Left side Right side d) n 4 Left Side ( 4 ) Right Side 4 + ( 4) Left side Right side e) x Left Side + 4 Right Side Left side Right side f) m 0 Left Side.(0) 7 Right Side (0) Left side Right side. a) m Left Side ( + ) Right Side ( ) ( ) ( ) 0 0 Left side Right side b) x Left Side 0.[() ]. Right Side 0.04( + ) 0.(9). 0.04(0) Left side Right side c) x Left Side 0( ) + 6 Right Side 4( ) Left side Right side d) m Left Side 4() 9 Right Side + 6 Left side Right side 4. a) The dimensions of the garden are 4 m by m. b) There were 9 quarters and dimes in the cash register. c) The employee will need 0 kg of cashews for the mixture. d) Plane A is travelling at 70 km/h, and Plane B is travelling at 00 km/h. BLM 8 Section 8.4 Math Link a).; m.m 0.87 or.m m b) Any three estimates around the amount of 0.8 mg. For example, students might guess mg or 6 mg. Students might look at the number 0.87 and see that it is close to is about times 60, so they might estimate 60. c) Example: m.m 0.87, m m, 0.87.m, 0.8 m. The mass of riboflavin in one small serving of raw almonds is 0.8 mg. d) Example: Isolating the variable because it was much quicker and more accurate. BLM 8 4 Chapter 8 Test. C. D. D a) b) 9 c). d) 9. a) x 08.0 b) 0 0. a) Alexandra did not apply the distributive property correctly. This step should be 4x 0 6. b) 9 d. a) 4 b). m c) 0.8 s 0. Copyright McGraw-Hill Ryerson, 009

9 . BLM 8 6. (continued) BLM 8 Chapter 8 Math Link: Wrap It Up! Example: a) One serving of canned salmon contains 0.8 MJ of energy. How many serving would you have to eat to get.00 MJ of energy? Let n number of servings. 0.8n.00 MJ. b) How many MJ of energy do 8 baked potatoes have? One potato has 0.94 MJ of energy. E Let E energy. 8, E 7. MJ 0.94 c) A baked potato with some cheddar cheese on it provides a total of.08 MJ of energy. How many 4 g servings of cheese is on the potato? Let x one serving of cheese: 0.76x , x., or 67. g of cheese d) Tinka and Jacob ate a bowl of Brazil nuts. Tinka ate. servings of the nuts. The total energy of the nuts in the bowl was 8. MJ. How many servings did Jacob eat? One serving of nuts is.0 MJ. Let j serving Jacob ate..0(j +.) 8., j. servings. e) Sara ate some cheddar cheese, and Anoop ate some mango. They each ate the same number of servings. The cheese provided Sara with 0.6 MJ more energy than the brazil nuts provided Anoop. How many servings did Sara and Anoop each eat? The energy in one serving of cheddar cheese is 0.76 MJ. The energy in one serving of mango is 0.48 MJ. Let s the number of servings they each ate. 0.76s 0.48s + 0.6, s servings. Copyright McGraw-Hill Ryerson, 009

Chapter 8 BLM Answers

Chapter 8 BLM Answers. BLM 8. BLM 8 Chapter 8 Math Link Introduction a) 0; 0;, so g b) 94; h w, s so (4) 94 c) %, or 0.; 0.., 80 so s 0 d) p + b; p +, so p e) 0 b + a; b + 0 0, so b 40 f) p ; ( ) p a +