A baseball team played 82 games. The team won 7 more than twice as many games as it lost. The equation l + 2l + 7 = 82 models this relationship, where l is the number of games lost. How many games did the team lose? How many games did the team win?
The Correct Answer and Explanation is:
We are given the equation that models the relationship between the number of games won and lost by the baseball team:l+2l+7=82l + 2l + 7 = 82l+2l+7=82
where:
- lll represents the number of games lost,
- 2l+72l + 72l+7 represents the number of games won, based on the fact that the team won 7 more than twice as many games as it lost,
- The total number of games played is 82.
Step 1: Solve for lll
First, combine like terms on the left-hand side of the equation:l+2l+7=82l + 2l + 7 = 82l+2l+7=823l+7=823l + 7 = 823l+7=82
Next, subtract 7 from both sides:3l=82−73l = 82 – 73l=82−73l=753l = 753l=75
Now, divide both sides by 3 to solve for lll:l=753l = \frac{75}{3}l=375l=25l = 25l=25
So, the team lost 25 games.
Step 2: Calculate the number of games won
We know from the problem that the team won 2l+72l + 72l+7 games. Now substitute l=25l = 25l=25 into this expression:Games won=2(25)+7=50+7=57\text{Games won} = 2(25) + 7 = 50 + 7 = 57Games won=2(25)+7=50+7=57
So, the team won 57 games.
Final Answer:
- The team lost 25 games.
- The team won 57 games.
Explanation:
The equation l+2l+7=82l + 2l + 7 = 82l+2l+7=82 expresses the total number of games as the sum of the games lost (lll) and the games won (2l+72l + 72l+7). Solving for lll gives the number of games lost, and using that result, we can find the number of games won. This gives a solution that satisfies the total number of 82 games played.
