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Chapter 11   

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Royal Teams

solution

Royals, 90%
Knights, 45%
Dukes, 40%
Crowns, 35%
Bishops, 25%

explanation

Step 1
Make a chart to record the information.
Team Points Fraction Percent
Royals      
Knights      
Dukes      
Crowns      
Bishops      

Step 2
Use the clues to find the number of points scored by each team.

  • Given: The Royals scored 54 of the possible 60 points.
  • The Knights scored 27 points, half as many points as the Royals
    (54 ÷ 2 = 27).
  • The Bishops scored 15 points, 12 fewer points than the Knights
    (27 – 12 = 15).
  • The Crowns scored 35% of the possible 60 points.
    (Since the final question asks about percent, which is given, you don't need to find the number of points scored by the Crowns, but you would find that by multiplying 0.35 by 60; the Crowns scored 21 points.)
  • The Dukes earned 2/5 of the possible points.
    (It is not necessary to find the number of points to solve the problem. If you wish to know the number of points the Dukes scored, multiply 2/5 by 60; 2/5 x 60 = 24.)

Step 3
To express each team's score as a percent, first express the score as a fraction. The numerator is the team's score. The denominator is the total number of possible points.

  • Royals: 54/60 = 9/10

  • Knights: 27/60 = 9/20

  • Bishops: 15/60 = 1/4

  • Dukes: 2_5 (given as a clue)

  • Crowns: 21/60 = 7/20 (not needed to answer the question)

Step 4
Write an equivalent ratio with a denominator of 100. Express that ratio as a percent.

  • Royals: 54/60 = 9/10 = 9/100 = 90%

  • Knights: 27/60 = 9/20 = 45/100 = 45%

  • Bishops: 15/60 = 1/4 = 25/100 = 25%

  • Dukes 2/5 = 40_100 = 40%

  • Crowns 35% (given)

Step 5
List the teams from first place to fifth place with the highest percent first.

  • Royals, 90%
  • Knights, 45%
  • Dukes, 40%
  • Crowns, 35%
  • Bishops, 25%

Expressing Each Score as a Percent
Team Points Fraction Equivalent ratio with denominator of 100 Percent
Royals 54 54/60 = 9/10 90
100
90%
Knights 27 27/60 = 9/20 45
100
45%
Dukes 24 24/60 = 2/5 40
100
40%
Crowns 21 21/60 = 7/20 35
100
35%
Bishops 15 15/60 = 1/4 25
100
25%

 


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