4 Two movies, together, run for 3 hours. One movie runs 12 minutes longer than the other. How long is each movie?

Transcription

1 Algebra Problems 1 A number is increased by 12. The resul is 28. A) Wrie an equaion o find he number. B) Solve your equaion o find he number. 2 A number is decreased by 6. The resul is 15. A) Wrie an equaion o find he number. B) Solve your equaion o find he number. 3 Two videos were played back o back for a oal lengh of 3 hours. One video runs 15 minues longer han he oher. How long is each movie? Name Hins: Always wrie he saemen: Le x represen... Le a variable be he number you are rying o find. If you have o find 2 hings in he quesion le he variable represen he smaller par. 4 Two movies, ogeher, run for 3 hours. One movie runs 12 minues longer han he oher. How long is each movie? 5 In a family inheriance of $ he daugher received $4 000 more han he son. How much did each receive? 6 Speed is calculaed by he formula s = d /. If a car was imed a a speed of 12 km/h for 156 km., how many hours has i ravelled? 7 A coa and pans cos $ The coa cos $6.00 more han he pans. How much did each iem cos? 8 Mary and Bey have saved $43.00 Bey has saved $3.00 more han he amoun Mary has saved. How much money has each girl saved? 9 A carpener cu a board ha was 10 m long ino wo pieces. The longer piece is 2 m longer han hree imes he lengh of he shorer piece. Wha is he lengh of each piece? 10 Brenda s age plus her siser, Susan s, age added ogeher is heir faher s age. A) Wrie an equaion o represen he saemen B) Wha is he faher s age is Brenda is 15 and Susan is 19? C) Wha is Brenda s age if her faher is 92 and her siser is 20? D) Wha is Susan s age if Brenda is 3 and her faher is 20? E) Are all hese answers realisic?

2 Answers 1 Le x represen he missing number x + 12 = 28 x = x = 16 x + 12 = 28 (16) + 12 = = 28 he missing number is 16 2 Le x represen he missing number x - 6 = 15 x = x = 21 x - 6 = 15 (21) - 6 = = 15 he missing number is 21 3 Le x represen he lengh of he shorer movie shor + long = 180 x + (x + 15) = 180 2x + 15 = 180 2x = x = 165 2x = 165 x = 82.5 Longer Movie x + ( x + 15) = 180 x + 15 = = 180 = = 180 = 97.5 Shor + long = 180 minues = = 180 he shorer movie is 82.5 minues long and he longer movie is

3 4 Le x represen he shorer movie shor + long = 180 x + (x + 12) = 180 2x + 12 = 180 2x = x = 168 2x = 168 x = 84 5 Le x represen he son s inheriance son + daugher = x + (x ) = x = x = x = x = = 2 x = Le represen he hours ravelled s = d 12 = = = = = 13 x + (x + 12) = = = 180 Long x + 12 = = 96 he shor movie was 84 minues long and he long movie was 96 minues long x + (x ) = ( ) = = = Daugher x = = he son will inheri $8 000 and he daugher will inheri $ s = d 12 = = 12 he car ravelled for 13 hours

4 7 Le x represen he cos of he pans pans + coa = cos x + (x + 6) = 28 2x + 6 = 28 2x = x = 22 2x = 22 x = 11 x + (x + 6) = 28 Coa = x (11 + 6) = 28 = = 28 = = 28 pans + coa = cos = = 28 he pans cos $11.00 and he coa coss 8 Le x represen Mary s savings Mary + Bey = Toal Savings x + (x + 3) = 43 2x + 3 = 43 2x = x = 40 2x = 40 x = 20 9 Le x represen he shorer piece of wood shor + long = oal x + (3x + 2) = 10 4x + 2 = 10 4x = x = 8 4x = x = 2

5 10 Le B represen Brenda, S represens Susan and F represen he faher A) Brenda + Susan = Faher B) B + S = F = F 34 = F C) B + S = F B + 20 = 92 B = B = 72 D) B + S = F 3 + S = S = 20-3 S = 17 The faher is 34 Brenda was 72 Susan was 17 E) How can he faher be 20 and he daugher be 17? Tha would mean he daugher was born when he faher was only 3.

6 Algebra Journal Name: Selec one quesion from he Algebra Problems page and complee his page. Wrie ou he quesion: Show all he seps you used o solve he problem Explain, in deail how and why you did each sep

7 Level 1 Level 2 Level 3 Level 4 Knowledge and Undersanding -demonsraes limied undersanding of conceps - demonsraes some undersanding of conceps - demonsraes undersanding of conceps - demonsraes horough undersanding of conceps Thinking Show all seps wih limied effeciveness wih some effeciveness wih effeciveness wih a high degree of effeciveness Communicaing Words you use convenions, erminology of he mahemaics wih limied effeciveness convenions, erminology of he mahemaics wih some effeciveness convenions, erminology of he mahemaics wih effeciveness convenions, erminology of he mahemaics wih a high degree of effeciveness Applicaion Show your answer makes sense connecions wihing and beween various conexs wih limied effeciveness connecions wihing and beween various conexs wih some effeciveness connecions wihing and beween various conexs wih effeciveness connecions wihing and beween various conexs wih a high degree of effeciveness