Question

a baseball team played 140 regular season games. the ratio of the number of games they won to the number of games they lost was \\(\frac{5}{2}\\). how many games did they win? how many games did they lose?
the team won \\(\boxed{100}\\) games. (type a whole number.)
the team lost \\(\square\\) games. (type a whole number.)

Explanation:

Step1: Define variables

Let the number of games won be $5x$ and the number of games lost be $2x$ (since the ratio of won to lost is $\frac{5}{2}$).

Step2: Total games equation

The total number of games is the sum of won and lost games, so $5x + 2x = 140$.

Step3: Solve for x

Combine like terms: $7x = 140$. Then divide both sides by 7: $x = \frac{140}{7} = 20$.

Step4: Find games lost

The number of games lost is $2x$. Substitute $x = 20$: $2\times20 = 40$.

Answer:

The team lost 40 games.