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:
Let’s break it down step by step. We’re told that the team won 84 games, and that they won 14 more games than they lost, with no ties.
Step 1: Define Variables
Let L represent the number of games the team lost. From the problem, we know that:
- The number of games won is 14 more than the number of games lost, so: Games won=L+14\text{Games won} = L + 14Games won=L+14
We are also given that the team won 84 games, so we can set up the equation: L+14=84L + 14 = 84L+14=84
Step 2: Solve for the Number of Games Lost (L)
To find the number of games the team lost, we can subtract 14 from both sides of the equation: L=84−14L = 84 – 14L=84−14 L=70L = 70L=70
So, the team lost 70 games.
Step 3: Calculate the Total Number of Games Played
The total number of games played is simply the sum of the games won and the games lost: Total games played=84 (won)+70 (lost)=154\text{Total games played} = 84 \, (\text{won}) + 70 \, (\text{lost}) = 154Total games played=84(won)+70(lost)=154
Final Answer
- The team lost 70 games.
- The total number of games played is 154.
Explanation:
We used a simple algebraic approach. We expressed the relationship between the games won and lost in terms of a single variable, then solved for that variable. After determining the number of games lost, we found the total number of games played by adding the wins and losses.
