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 \( w \) be the number of games won and \( l \) be the number of games lost. We know that \( w + l = 140 \) (total games) and the ratio \( \frac{w}{l}=\frac{5}{2} \), so \( w=\frac{5}{2}l \).

Step2: Substitute and solve for \( l \)

Substitute \( w=\frac{5}{2}l \) into \( w + l = 140 \):
\[
\frac{5}{2}l + l = 140
\]
Combine like terms:
\[
\frac{5}{2}l+\frac{2}{2}l = 140 \implies \frac{7}{2}l = 140
\]
Multiply both sides by \( \frac{2}{7} \):
\[
l = 140\times\frac{2}{7}=40
\]

Step3: Find \( w \)

Since \( w + l = 140 \) and \( l = 40 \), then \( w = 140 - 40 = 100 \). (This matches the given won games, so we can confirm the lost games calculation.)

Answer:

The team lost \(\boldsymbol{40}\) games.