Rahul, a coach at a local school has collected data on his players. But in an accident he lost how many games each player participated in. He knows that per game Michael played 30 minutes, had 1 foul, and 2 goals. Per game, Sherry played 25 minutes, had 1 foul, and 5 goals. Rashad played 20 minutes, had 2 fouls, and 4 goals per game. Rahul also knows that the total amount of all three players. Together they played 370 minutes, had 20 fouls, and 58 goals. Can you use algebra to determine how many games each athlete played in

Michael played 4 games, Sherry played 6 games and Rashad played 5 games

Step-by-step explanation:

Let X, Y and Z represents the  number of games for the three players.

Based on the given information, three equations can be formed -

30 X + 25 Y + 20 Z = 370 ---(1)

X + Y + 2Z = 20 ---(2)

2X + 5Y + 4 Z = 58 ---(3)

From Equation (2), X = 20 -Y-2Z

Substituting value of X from equation 2, in equation 1 and 2, we get -

30 (20-Y-2Z) + 25 Y + 20 Z = 370

600 -30Y-60Z + 25 Y + 20 Z = 370

-5Y -40Z = -230

Y + 8Z = 46 (4)

2(20-Y-2Z) + 5Y + 4 Z = 58

40 -2Y-4Z + 5Y + 4 Z = 58

3Y = 18

Y = 6

Substituting value of Y in equation 4, we get -

8Z = 46-6

8Z = 40

Z = 5

Substituting value of Y and Z in equation 2 we get

X + 6 + 2* 5 = 20

X = 20-16 = 4

Hence, Michael played 4 games, Sherry played 6 games and Rashad played 5 games

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