Extra Practice 1. Name Date. Lesson 6.1: Solving Equations Using Models

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1 Maser 6.0 Era Pracice Lesson 6.: Solving Equaions Using Models. Use a model o solve each equaion. Verif he soluion. a) 7 = 56 b) 45 = 9 c) = 4 d) 9 =. Use a model o solve each equaion. Verif he soluion. a) = 44 b) 7 + = c) 0 = 4 6 d) + 8 = 0. Five less han si imes a number is. Le n represen he number. a) Wrie an equaion ou can use o solve for n. b) Use a model o solve he equaion. Wha is he number? c) Verif he soluion. 4. Jack and Diane wen o he movies. The each paid he same amoun for an admission icke. Togeher, he spen $ on snacks. The oal cos of admission and snacks for Jack and Diane was $6. How much was each admission icke? a) Choose a variable. Wrie an equaion ou could use o solve his problem. b) Use a model o solve he equaion. c) Verif he soluion. 5. Use a model o solve each equaion. Verif he soluion. a) 4 + = b) 4 + = c) 4 = d) 4 = e) 4 = f) 4 =

2 Maser 6. Era Pracice Lesson 6.: Solving Equaions Using Algebra. Solve each equaion. Verif he soluion. a) 4 = b) 5 = 5 c) 48 = 8 d) 9 = 54. Solve each equaion. Verif he soluion. a) 8a + = 7 b) b + = 9 c) 4 = 5c 7 d) 6f 5 = 45. Solve each equaion. Verif he soluion. a) 7 = 9 b) = 4 c) 6 7 = 9 d) 7 8 = 4. Solve each equaion. Verif he soluion. a) a + = 4 b) 5 = 0 + b c) = 5c 6 d) 9f 7 = 5. Wrie an equaion ou can use o answer each quesion. Solve he equaion. Verif he soluion. a) Five more han wo imes a number is 7. Wha is he number? b) Si less han five imes a number is 9. Wha is he number? 6. The Grade 8 sudens had a graduaion dinner. The paid a fla rae of $5 for he use of he hall, plus $ for each suden who aended. The oal cos of he dinner was $944. How man sudens aended he dinner? a) Wrie an equaion ou could use o solve he problem. b) Solve he equaion. Verif he soluion. 7. Use his informaion: Ice renal: $50 Skae renal: $ a) Wrie a problem ha can be solved using an equaion. b) Wrie he equaion, hen solve he problem. The righ o reproduce his page is resriced o purchasing schools.

3 Maser 6. Era Pracice Lesson 6.: Solving Equaions Involving Fracions. Solve each equaion. Verif he soluion. a a) = 7 b) = 9 4 c) 7 b = d) 6 c =. Solve each equaion. Verif he soluion. d f a) = 8 b) = c) k q = d) = -. One-quarer of he chicken pieces in he dish are wings. There are 7 wings. How man chicken pieces are in he dish? a) Wrie an equaion ou can use o solve he problem. b) Solve he equaion. c) Verif he soluion. 4. Solve each equaion. Verif he soluion. a) n = 0 b) 4 5 p = c) = 5 d) 7 + n = 9-5. For each senence, wrie an equaion. Solve he equaion o find he number. a) A number divided b 4 is 7. b) Add 4 o a number divided b and he sum is. c) Subrac a number divided b 6 from and he difference is Check his suden s work. Rewrie a correc and complee algebraic soluion if necessar = 4 = = = 8

4 Maser 6. Era Pracice 4 Lesson 6.4: The Disribuive Proper. Draw a recangle o show ha 7( + ) and 7 + are equivalen.. Draw algebra iles o show ha (n 5) and n 0 are equivalen.. Epand. a) 5( + 6) b) 7(5 e) c) ( + 8) d) 4(6 e) e) 8( n + 4) f) ( + 7) g) 7(5n 4) h) 4( + ) 4. Loer ickes are sold b a local chari o raise mone for cancer research. Each icke coss $00. Some people pa wih a $00 bill and some pa wih a $00 cheque. Wrie wo epressions ou can use o calculae he oal amoun of mone colleced. Le b represen he number of $00 bills received. Le c represen he number of $00 cheques received. 5. Which pairs of epressions are equivalen? Eplain our reasoning. a) and 4( + 5) b) c + 4 and 4 + c c) 4 + b and 6b d) (a + 5) and 8 + a 6. A school uniform consiss of a shir and a pair of shors. A shir coss $. A pair of shors coss $5. a) Wrie wo differen epressions o find he cos of suppling 8 sudens wih uniforms. b) Evaluae each epression. Which epression did ou find easier o evaluae? Jusif our choice. 7. Epand. a) ( ) b) (9a 5 6) c) 9( 4 7c + 0) The righ o reproduce his page is resriced o purchasing schools.

5 Maser 6.4 Era Pracice 5 Lesson 6.5: Solving Equaions Involving he Disribuive Proper. Solve each equaion using he disribuive proper. Verif he soluion. a) 5(a + ) = 5 b) 4(p 6) = 4 c) 0( + ) = 0 d) 7(r 6) = 7. Solve each equaion. Verif he soluion. a) 7(b + 6) = 84 b) 5(q ) = 70 c) 9(d ) = 45 d) 6(f 5) = 6. A he fair, 5 friends each bough an $8 meal voucher and one ice-cream voucher. The oal cos of he vouchers was $55. Wha was he price of an ice-cream voucher? a) Choose a variable o represen he price of an ice-cream voucher. Wrie an equaion o model his problem. b) Solve he equaion using he disribuive proper. c) Verif he soluion. Eplain our hinking in words. 4. Sco bough 54 m of fencing o enclose a recangular plo of land. The widh of he recangular plo is m. Assume Sco uses all he fencing. Wha is he lengh of he recangular plo of land? a) Choose a variable o represen he lengh of he recangular plo of land. Wrie an equaion o model his problem. b) Solve he equaion using he disribuive proper. c) Verif he soluion. Eplain our hinking in words. 5. Heaher chose an ineger. She added 9, hen muliplied he sum b 4. The produc was 6. Which ineger did Heaher choose? a) Wrie an equaion ou can use o solve he problem. b) Solve he equaion. c) Verif he soluion. 6. Solve each equaion. Verif he soluion. a) 7(a + ) = 4 b) 5(7 r + ) = 0 c) 7(b ) = d) 6( + 5) = 0

6 Maser 6.5 Era Pracice 6 Lesson 6.6: Creaing a Table of Values. Cop and complee each able of values. a) = + 5 b) = c) = 4 5. Cop and complee each able of values. a) = 5 b) = + c) = The equaion of a linear relaion is: = + 8 Some ordered pairs in he relaion are: (, ), (0, 8), (, ), (, ), (, ), (4, ) Find he missing numbers in he ordered pairs. 4. The cos of admission o a fair is $0, plus $ per ride. An equaion for his relaion is C = 0 + r, where r represens he number of rides a person goes on, and C represens he oal cos of admission and rides. a) Use he equaion o creae a able of values. b) Harve wen on rides. How much did Harve spend on admission and rides? c) Sephanie spen $ on admission and rides. How man rides did Sephanie go on? 5. These ordered pairs are in he same linear relaion. (, ), (, 9), (, ), (0, 5), (, ), (, ), (, ) Find he missing numbers in he ordered pairs. Describe he sraeg ou used. The righ o reproduce his page is resriced o purchasing schools.

7 Maser 6.6 Era Pracice 7 Lesson 6.7: Graphing Linear Relaions. Each graph below is a graph of a linear relaion. Describe he relaionship beween he variables in each graph. a) = 6 + b) = 5. Graph each relaion for ineger values of from o. a) = b) = c) = + 5 d) = + 5. Here is a graph of he linear relaion = + 8. Each poin on he graph is labelled wih an ordered pair. Some numbers in he ordered pairs are missing. Find he missing numbers. Eplain how ou did his. 4. The cos of admission o a fair is $0, plus $ per ride. An equaion for his relaion is C = 0 + r, where r represens he number of rides a person goes on, and C represens he oal cos of admission and rides. a) Make a able of values for he relaion. b) Graph he relaion. c) Describe he relaionship beween he variables in he graph. d) Find he ordered pair on he graph ha shows he number of rides Josh wen on when his cos of admission and rides was $.

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9 Maser 6.7 Era Pracice Answers Era Pracice Maser 6.0 Lesson 6.. a) = 8 b) = 5 c) = 4 d) =. a) = 8 b) = c) = 9 d) = 4. a) 6n 5 = b) n = ; he number is. c) Lef side = 6() 5 = 8 5 = = Righ side 4. a) Le c represen he cos of admission. An equaion is: c + = 6 b) n = 7; each admission icke was $7.00. c) L.S. = (7) + = 4 + = 6 = R.S. 5. a) = 5 b) = 5 c) = 5 d) = 5 e) = 9 f) = 9 Era Pracice Maser 6. Lesson 6.. a) = 8 b) = 7 c) = 6 d) = 6. a) a = b) b = 6 c) c = d) f = 5. a) = 8 b) = 5 c) = d) = 4. a) a =, or 0.5 b) b = 5, or.5 c) c = 9 5, or.8 d) f = Le n represen he number. a) n + 5 = 7; n = 6 b) 5n 6 = 9; n = 7 6. a) Le n represen he number of sudens. 5 + n = 944 b) n = 6; 6 sudens Lef side = 5 + n = 5 + (6) = = 944 = Righ side 7. a) Ice renal a he local skaing rink is $50 for h. Skae renal is $ per person. The Grade 8 class wen skaing. All sudens rened skaes. The oal cos was $. How man sudens wen skaing? b) 50 + n = n = 7; 7 sudens wen skaing. Era Pracice Maser 6. Lesson 6.. a) = 8 b) a = 7 c) b = 77 d) c = 7. a) d = 40 b) f = 60 c) k = d) q = 6. Le c represen he number of chicken pieces in he dish. a) 4 c = 7 b) c = 8, here are 8 chicken pieces in he dish. c) I makes sense because 4 of he pieces are wings and 4 of 8 is a) n = 6 b) p = 45 c) = 7 d) n = 78 n 5. a) = 7; n = 8-4 n b) + 4 = ; n = 8 - n c) = 5; n = The soluion is correc unil he las line. The suden muliplied he lef side b 6 and divided he righ side b 6. Boh sides should have been muliplied b 6. = 8-6 Then, ( 6)( = 08-6 ) = (8)( 6) Era Pracice 4 Maser 6. Lesson a) b) 5 7e c) + 4 d) 4 + 4e e) 6n + f) g) 5n 8 h) (b + c) or 00b + 00c 5. a) Yes; 4( + 5) = 4 + 4(5) = b) Yes; when ou add, order does no maer. c) No; onl like erms can be added. Since 4 and b are no like erms, 4 + b ¹ 6b d) No; (a + 5) = a + 5 ¹ 8 + a 6. a) 8() + 8(5) or 8( + 5) b) 8() + 8(5) = = 96 8( + 5) = 8(7) = a) 8 + 0

10 b) 7a c) 6c 54 Era Pracice 5 Maser 6.4 Lesson 6.5. a) a = b) p = 5 c) = d) r = 7. a) b = 6 b) q = c) d = 8 d) f =. Le i represen he price of one ice-cream voucher in dollars. a) 5(8 + i) = 55 b) i = ; each ice-cream voucher was $. c) $ makes sense because he cos of a meal voucher and an ice-cream voucher is $8 + $ = $. There were 5 friends, so he oal cos of he vouchers would be 5 $ = $ a) Le l represen he lengh of he recangular plo of land in meres. 54 = (l + ) b) l = 5; he plo of land has lengh 5 m. c) 5 m makes sense because he perimeer of he recangular plo of land is: 5 m + m + 5 m + m = 54 m 5. a) Le i represen he ineger. 4(i + 9) = 6 b) i = 5; he ineger is 5. c) Lef side = 4( 5 + 9) = 4(4) = 6 = Righ side a) a = b) r = 0c) b = d) = 7 Era Pracice 6 Maser 6.5 Lesson 6.6. a) b) c). a) b) c) (, 5), (, ), (4, 4) 4. a) r C b) $49 c) Sephanie wen on 7 rides. The righ o reproduce his page is resriced o purchasing schools.

11 5. (, 7), (, ), (, ), (, ) I looked a he number paerns:,,, 0,,, and, 9, 7, 5,,, d) Era Pracice 7 Maser 6.6 Lesson 6.7. a) As increases b, decreases b 6. The graph is a line ha goes down o he righ. b) As increases b, increases b 5. The graph is a line ha goes up o he righ.. a) b). (, ), (, 6), (, 4) I used he paerns in he graph: As increases b, decreases b. 4. a) r C b) c) c) As r increases b, C increases b. The graph is a line ha goes up o he righ. d) (4, ); Josh rode on 4 rides.