Algebra 1 Common Core Student Edition, Grade 8-9

28. Reasoning A toy store w orker packed two boxes of identical dolls a n d p lu sh toys
    for shipping in boxes th at w eigh 1 oz w h en em pty. O ne box held 3 dolls a n d 4 plush
    toys. The w orker m arked th e w eight as 12 oz. The o th er box held 2 dolls a n d 3 plush
    toys. The w orker m arked th e w eight as 10 oz. Explain why th e w orker m u st have
    m ad e a mistake.
    2 9. E rro r A n alys is A stu d en t solved a system of eq u a tio n s by elim ination. D escribe
    an d correct th e error m ad e in th e p a rt of th e solution shown.


29. Nutrition Half a p ep p e ro n i pizza plus three fourths of a h am -a n d -p in eap p le
    pizza contains 765 Calories. O ne fourth of a p ep p e ro n i pizza plus a w hole ham -
    an d -p in e ap p le pizza contains 745 Calories. How m any Calories are in a w hole
    p ep p ero n i pizza? How m any Calories are in a w hole h am -a n d -p in e a p p le pizza?


30. Open-Ended Write a system of eq u atio n s th a t can b e solved efficiently by
    elim ination. Explain w hat you w ould do to elim inate one of th e variables. Then
    solve th e system.

Solve each system using any method. Explain why you chose the method you used.

32. y = 2.5x 33. 2x + y = 4 34. 3x + 2y = 5
    2y + 3x = 32


33. y = |x + 1
    2x + 3y = 27

6x + ly = 12

36. x + y = 1.5

2x + y = 1

4x + 5y = 16

37. | x + | y = 0

2X + 5y:

11

5

38. Compare and Contrast W hat do th e su b stitu tio n m e th o d an d th e elim ination
    m eth o d have in com m on? Explain. Give an exam ple of a system th a t you would
    prefer to solve using one m eth o d in stead of th e other. Justify your choice.


39. Vacations A hotel offers two activity packages. O ne costs $192 a n d includes 3 h of
    h orseback riding a n d 2 h of parasailing. The seco n d costs $213 an d includes 2 h of
    h orseback riding an d 3 h of parasailing. W hat is th e cost for 1 h of each activity?


40. Geometry Each of th e squares in th e figures show n at th e right h as the
    sam e area, an d each of th e triangles has th e sam e area. The total area of
    Figure A is 141 cm2. The total area of Figure B is 192 cm 2. W hat is th e area
    of each square a n d each triangle?

Challenge Solve each system using elimination.

42. 2x = 5(2 — y)
    y = 3 ( - x + 5)

41 - — - = —5x y °

• 
  
  
  
  • 
    
    
    
    • = 14
    
    
    
    
    
    
    43. 2x — 3y + z = 0
        2x + y + z = 12
        y —z = 4