MP.4 Model with Math A professional baseball team won 84 games this season. The team won 14 more games than it lost. There were no ties. How many games did the team lose? How many did it play?
The Correct Answer and Explanation is :
We are given that a professional baseball team won 84 games this season, and it won 14 more games than it lost. There were no ties. We need to determine how many games the team lost and how many games it played in total.
Let’s define two variables to represent the unknowns:
- Let ( x ) represent the number of games the team lost.
- Since the team won 14 more games than it lost, the number of games the team won is ( x + 14 ).
We also know that the total number of games the team played is the sum of the games it won and lost. Therefore, the total number of games played is:
[
x + (x + 14) = 84 + x
]
From the problem, we are told the team won 84 games, so:
[
x + 14 = 84
]
Now, solving for ( x ), we subtract 14 from both sides:
[
x = 84 – 14
]
[
x = 70
]
Thus, the team lost 70 games.
To find the total number of games played, we add the number of games won and the number of games lost:
[
84 + 70 = 154
]
Therefore, the team played a total of 154 games.
Final Answer:
- The team lost 70 games.
- The team played 154 games.
This problem involves setting up an equation based on the relationship between the wins, losses, and total games played, and solving it step by step.
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