Final answer:
To determine the number of games won and lost by the team, a system of equations was set up based on the given ratio and total games played. After solving the system, it was found that the team won 105 games and lost 42 games.
Step-by-step explanation:
The baseball team played a total of 147 regular season games, and the ratio of the number of games they won to the number of games they lost was given as five halves (5:2). To find out the exact number of games won and games lost, you can set up two variables: let w represent the number of games won and l represent the number of games lost.
According to the ratio, w / l = 5/2, and the sum of games won and lost is w + l = 147. To solve the system of equations, you multiply the second equation by 2 to make the coefficient of l the same as in the first equation: 2w + 2l = 294.
Now substitute 5l for 2w based on the ratio, which gives us 5l + 2l = 294, leading to 7l = 294. Divide by 7 to find l, which equals 42. Then substitute l back into w / l = 5/2 to find w: 5/2 * 42 = 105. So the team won 105 games and lost 42 games.