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 two-fifths 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 two-fifths by 60; two-fifths 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: fifty-four-sixtieths = nine-tenths

  • Knights: twenty-seven-sixtieths = nine-twentieths

  • Bishops: fifteen-sixtieths = one-fourth

  • Dukes: two-fifths (given as a clue)

  • Crowns: twenty-one-sixtieths = seven-twentieths (not needed to answer the question)

Step 4

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

  • Royals: fifty-four-sixtieths = nine-tenths = nine-hundredths = 90%

  • Knights: twenty-seven-sixtieths = nine-twentieths = forty-five-hundredths = 45%

  • Bishops: fifteen-sixtieths = one-fourth = twenty-five-hundredths = 25%

  • Dukes two-fifths = forty-hundredths = 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 fifty-four-sixtieths = nine-tenths 90
100
90%
Knights 27 twenty-seven-sixtieths = nine-twentieths 45
100
45%
Dukes 24 twenty-four-sixtieths = two-fifths 40
100
40%
Crowns 21 twenty-one-sixtieths = seven-twentieths 35
100
35%
Bishops 15 fifteen-sixtieths = one-fourth 25
100
25%


Houghton Mifflin Math Grade 5