Question

(Set up and solve the system, then answer the associated question)

Answer 1

9514 1404 393

Answer:

• red division: 6 teams
• blue division: 5 teams

Step-by-step explanation:

We can let r and b represent the numbers of teams in the red and blue divisions, respectively. The total number of goals scored in each division will be the average for that division times the number of teams in that division.

  r - b = 1 . . . . . . there is 1 more red team than blue

  4.5r +4.2b = 48 . . . . . . total goals scored per week

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Solving by substitution, we have ...

  r = b +1

  4.5(b +1) +4.2b = 48 . . . . substitute for r

  8.7b +4.5 = 48 . . . . . . . . simplify

  8.7b = 43.5 . . . . . . . . . . subtract 4.5

  b = 43.5/8.7 = 5 . . . . . divide by 8.7

  r = b +1 = 6 . . . . . . . . . find r

There are 6 red teams and 5 blue teams.

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Additional comment

The basic idea is that you make an equation for each relation given in the problem statement. For a problem like this, you do need to have an understanding of how the average number of goals would be calculated and how that relates to the total goals.