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

An indoor soccer team has a blue and a red division. There is one more team in the red division than the blue division. The average number of goals scored per week in the blue division is 4.2 and the average number of goals scored per week in the red division is 4.5. The average number of goals scored per week in both leagues combined is 48 total goals. How many teams are in each division?

(I think I’m mostly stuck on how I would set this problem up, but I would appreciate any help at all!! Thank you ^^)

Sagot :

sqdancefan

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.

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